Computational algorithm for solving fredholm time-fractional partial integrodifferential equations of dirichlet functions type with error estimates
Numerical modeling of partial integrodifferential equations of fractional order shows interesting properties in various aspects of science, which means increased attention to fractional calculus. This paper is concerned with a feasible and accurate technique for obtaining numerical solutions for a c...
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| Veröffentlicht in: | Applied mathematics and computation Jg. 342; S. 280 - 294 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Elsevier Inc
01.02.2019
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| ISSN: | 0096-3003, 1873-5649 |
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| Abstract | Numerical modeling of partial integrodifferential equations of fractional order shows interesting properties in various aspects of science, which means increased attention to fractional calculus. This paper is concerned with a feasible and accurate technique for obtaining numerical solutions for a class of partial integrodifferential equations of fractional order in Hilbert space within appropriate kernel functions. The algorithm relies on the reproducing kernel Hilbert space method that provides the solutions in rapidly convergent series representations for the reproducing kernel based upon the Fourier coefficients of orthogonalization process. The Caputo fractional derivatives are introduced to address these issues. Moreover, the error estimate of the generated solutions is established as well as the convergence of the iterative method is investigated under some theoretical assumptions. The superiority and applicability of the present technique is illustrated by handling linear and nonlinear numerical examples. The outcomes obtained are compared with exact solutions and existing methods to confirm the effectiveness of the reproducing kernel method. |
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| AbstractList | Numerical modeling of partial integrodifferential equations of fractional order shows interesting properties in various aspects of science, which means increased attention to fractional calculus. This paper is concerned with a feasible and accurate technique for obtaining numerical solutions for a class of partial integrodifferential equations of fractional order in Hilbert space within appropriate kernel functions. The algorithm relies on the reproducing kernel Hilbert space method that provides the solutions in rapidly convergent series representations for the reproducing kernel based upon the Fourier coefficients of orthogonalization process. The Caputo fractional derivatives are introduced to address these issues. Moreover, the error estimate of the generated solutions is established as well as the convergence of the iterative method is investigated under some theoretical assumptions. The superiority and applicability of the present technique is illustrated by handling linear and nonlinear numerical examples. The outcomes obtained are compared with exact solutions and existing methods to confirm the effectiveness of the reproducing kernel method. |
| Author | Arqub, Omar Abu Al-Smadi, Mohammed |
| Author_xml | – sequence: 1 givenname: Mohammed orcidid: 0000-0003-0226-7254 surname: Al-Smadi fullname: Al-Smadi, Mohammed organization: Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, Jordan – sequence: 2 givenname: Omar Abu orcidid: 0000-0001-9526-6095 surname: Arqub fullname: Arqub, Omar Abu email: o.abuarqub@ju.edu.jo organization: Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan |
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| Cites_doi | 10.1007/s00521-015-2110-x 10.1016/j.camwa.2016.11.032 10.1090/S0002-9947-1950-0051437-7 10.1108/HFF-07-2016-0278 10.1016/j.amc.2014.12.121 10.1002/num.21809 10.1155/2014/431965 10.1016/j.amc.2014.04.057 10.1016/j.aml.2013.05.006 10.3233/FI-2016-1384 10.1016/j.cam.2013.04.040 10.1016/j.jcp.2014.08.004 10.1002/num.22209 10.1002/num.22236 10.1007/s00500-016-2262-3 10.1016/j.cam.2009.01.012 10.3390/e18060206 10.1007/s00009-017-0904-z 10.1186/s13662-017-1085-6 10.1016/S0165-1684(03)00181-6 10.1016/j.amc.2017.08.048 10.1016/j.amc.2013.03.006 10.1155/2013/608943 10.1016/j.jaubas.2014.02.002 10.1016/j.aml.2011.10.025 10.1155/2014/162896 10.1007/s00500-015-1707-4 10.1016/j.camwa.2016.01.001 10.1016/j.camwa.2011.03.037 10.3390/e16010471 10.1016/j.amc.2014.06.063 10.1016/j.apm.2015.01.021 10.1002/mma.3884 10.1007/s00521-016-2484-4 10.1016/j.jcp.2014.09.034 10.1016/j.amc.2013.03.123 10.1016/j.aml.2005.10.010 |
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| Keywords | Partial integrodifferential equation Computational algorithm Fredholm operator Caputo fractional derivative Fractional calculus theory |
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| References | Momani, Abu Arqub, Hayat, Al-Sulami (bib0039) 2014; 240 Geng, Qian (bib0048) 2013; 26 Abu Arqub, Al-Smadi, Momani, Hayat (bib0040) 2016; 20 El-Ajou, Abu Arqub, Momani, Baleanu, Alsaedi (bib0017) 2015; 257 Mohammed (bib0010) 2014 Jiang, Chen (bib0049) 2014; 30 Abu Arqub, Maayah (bib0044) 2018; 29 Cui, Lin (bib0027) 2009 Ray (bib0019) 2016; 71 Geng, Qian (bib0053) 2015; 39 Zaremba (bib0021) 1907; 39 Abu Arqub (bib0036) 2016; 39 Arshed (bib0007) 2017 Podlubny (bib0003) 1999 Zaslavsky (bib0002) 2005 Daniel (bib0029) 2003 Abu Arqub (bib0042) 2017; 28 Shawagfeh, Abu Arqub, Momani (bib0047) 2014; 16 Abu Arqub, Al-Smadi (bib0038) 2014; 243 Geng, Qian, Li (bib0050) 2014; 255 Abu Arqub (bib0045) 2018; 28 Samko, Kilbas, Marichev (bib0004) 1993 Wang, Zhu (bib0015) 2017; 2017 A. Kilbas, H. Srivastava, J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, Netherlands, 2006. Ortigueira, Machado (bib0020) 2003; 83 Zhoua, Cui, Lin (bib0032) 2009; 230 Yang, Lin (bib0033) 2008; 2008 Huang, Li, Zhao, Duan (bib0009) 2011; 62 Abu Arqub (bib0043) 2016; 146 Jiang, Chen (bib0052) 2013; 219 El-Ajou, Abu Arqub, Momani (bib0018) 2015; 293 Kumar, Singh, Kılıçman (bib0022) 2013 Abu Arqub, Shawagfeh (bib0046) 2017 Weinert (bib0030) 1982 Mainardi (bib0001) 2010 Rostami, Maleknejad (bib0008) 2017; 14 Singh, Kumar, Swroop, Kumar (bib0023) 2017 Aronszajn (bib0026) 1950; 68 Geng, Cui (bib0051) 2012; 25 Singh, Kumar, Nieto (bib0025) 2016; 18 Abu Arqub, Al-Smadi, Shawagfeh (bib0037) 2013; 219 Abu Arqub, Al-Smadi, Momani, Hayat (bib0041) 2017; 21 Singh, Kumar, Hammouch, Atangana (bib0006) 2018; 316 Tohidi, Ezadkhah, Shateyi (bib0012) 2014 Abu Arqub, El-Ajou, Al Zhour, Momani (bib0013) 2014; 16 Berlinet, Agnan (bib0028) 2004 Abu Arqub (bib0034) 2017; 73 Abu Arqub, Rashaideh (bib0035) 2017 Lin, Cui, Yang (bib0031) 2006; 19 Abu Arqub, El-Ajou, Momani (bib0016) 2015; 293 Abu Arqub, Al-Smadi (bib0011) 2018; 34 Kumar, Singh, Kumar (bib0024) 2015; 17 Abu Arqub (bib0014) 2018; 34 Mohammed (10.1016/j.amc.2018.09.020_bib0010) 2014 Momani (10.1016/j.amc.2018.09.020_bib0039) 2014; 240 Abu Arqub (10.1016/j.amc.2018.09.020_bib0034) 2017; 73 Abu Arqub (10.1016/j.amc.2018.09.020_bib0038) 2014; 243 El-Ajou (10.1016/j.amc.2018.09.020_bib0017) 2015; 257 Abu Arqub (10.1016/j.amc.2018.09.020_bib0041) 2017; 21 Abu Arqub (10.1016/j.amc.2018.09.020_bib0046) 2017 Kumar (10.1016/j.amc.2018.09.020_bib0022) 2013 Abu Arqub (10.1016/j.amc.2018.09.020_bib0037) 2013; 219 Abu Arqub (10.1016/j.amc.2018.09.020_bib0044) 2018; 29 Zaremba (10.1016/j.amc.2018.09.020_bib0021) 1907; 39 10.1016/j.amc.2018.09.020_bib0005 Geng (10.1016/j.amc.2018.09.020_bib0051) 2012; 25 Shawagfeh (10.1016/j.amc.2018.09.020_bib0047) 2014; 16 Mainardi (10.1016/j.amc.2018.09.020_bib0001) 2010 Jiang (10.1016/j.amc.2018.09.020_bib0052) 2013; 219 Abu Arqub (10.1016/j.amc.2018.09.020_bib0011) 2018; 34 Jiang (10.1016/j.amc.2018.09.020_bib0049) 2014; 30 Samko (10.1016/j.amc.2018.09.020_bib0004) 1993 Cui (10.1016/j.amc.2018.09.020_bib0027) 2009 Tohidi (10.1016/j.amc.2018.09.020_bib0012) 2014 Arshed (10.1016/j.amc.2018.09.020_bib0007) 2017 Abu Arqub (10.1016/j.amc.2018.09.020_bib0014) 2018; 34 Lin (10.1016/j.amc.2018.09.020_bib0031) 2006; 19 Abu Arqub (10.1016/j.amc.2018.09.020_bib0013) 2014; 16 Geng (10.1016/j.amc.2018.09.020_bib0053) 2015; 39 Singh (10.1016/j.amc.2018.09.020_bib0023) 2017 Ortigueira (10.1016/j.amc.2018.09.020_bib0020) 2003; 83 Berlinet (10.1016/j.amc.2018.09.020_bib0028) 2004 Weinert (10.1016/j.amc.2018.09.020_bib0030) 1982 Huang (10.1016/j.amc.2018.09.020_bib0009) 2011; 62 Yang (10.1016/j.amc.2018.09.020_bib0033) 2008; 2008 Abu Arqub (10.1016/j.amc.2018.09.020_bib0035) 2017 Abu Arqub (10.1016/j.amc.2018.09.020_bib0040) 2016; 20 Geng (10.1016/j.amc.2018.09.020_bib0048) 2013; 26 Abu Arqub (10.1016/j.amc.2018.09.020_bib0043) 2016; 146 Geng (10.1016/j.amc.2018.09.020_bib0050) 2014; 255 Podlubny (10.1016/j.amc.2018.09.020_bib0003) 1999 Daniel (10.1016/j.amc.2018.09.020_bib0029) 2003 Kumar (10.1016/j.amc.2018.09.020_bib0024) 2015; 17 Rostami (10.1016/j.amc.2018.09.020_bib0008) 2017; 14 Ray (10.1016/j.amc.2018.09.020_bib0019) 2016; 71 El-Ajou (10.1016/j.amc.2018.09.020_bib0018) 2015; 293 Wang (10.1016/j.amc.2018.09.020_bib0015) 2017; 2017 Abu Arqub (10.1016/j.amc.2018.09.020_bib0036) 2016; 39 Zaslavsky (10.1016/j.amc.2018.09.020_bib0002) 2005 Singh (10.1016/j.amc.2018.09.020_bib0006) 2018; 316 Abu Arqub (10.1016/j.amc.2018.09.020_bib0016) 2015; 293 Abu Arqub (10.1016/j.amc.2018.09.020_bib0045) 2018; 28 Singh (10.1016/j.amc.2018.09.020_bib0025) 2016; 18 Zhoua (10.1016/j.amc.2018.09.020_bib0032) 2009; 230 Abu Arqub (10.1016/j.amc.2018.09.020_bib0042) 2017; 28 Aronszajn (10.1016/j.amc.2018.09.020_bib0026) 1950; 68 |
| References_xml | – year: 1993 ident: bib0004 article-title: Fractional Integrals and Derivatives Theory and Applications – volume: 26 start-page: 998 year: 2013 end-page: 1004 ident: bib0048 article-title: Reproducing kernel method for singularly perturbed turning point problems having twin boundary layers publication-title: Appl. Math. Lett. – start-page: 1 year: 2017 end-page: 8 ident: bib0023 article-title: An efficient computational approach for time-fractional Rosenau–Hyman equation publication-title: Neural Computing and Applications – volume: 30 start-page: 289 year: 2014 end-page: 300 ident: bib0049 article-title: A collocation method based on reproducing kernel for a modified anomalous subdiffusion equation publication-title: Numerical Methods for Partial Differential Equations – volume: 316 start-page: 504 year: 2018 end-page: 515 ident: bib0006 article-title: A fractional epidemiological model for computer viruses pertaining to a new fractional derivative publication-title: Appl. Math. Comput. – year: 2014 ident: bib0012 article-title: Numerical solution of nonlinear fractional Volterra integro-differential equations via Bernoulli polynomials publication-title: Abstract and Applied Analysis – year: 1982 ident: bib0030 article-title: Reproducing Kernel Hilbert Spaces: Applications in Statistical Signal Processing publication-title: Hutchinson Ross – year: 2013 ident: bib0022 article-title: An Efficient Approach for Fractional Harry Dym Equation by Using Sumudu Transform publication-title: Abstract and Applied Analysis – volume: 2017 start-page: 27 year: 2017 ident: bib0015 article-title: Solving nonlinear Volterra integro-differential equations of fractional order by using Euler wavelet method publication-title: Advances in Difference Equations – year: 2017 ident: bib0007 article-title: B-spline solution of fractional integro partial differential equation with a weakly singular kernel publication-title: Numerical Methods for Partial Differential Equations – volume: 293 start-page: 385 year: 2015 end-page: 399 ident: bib0016 article-title: Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations publication-title: J. Comput. Phys. – volume: 25 start-page: 818 year: 2012 end-page: 823 ident: bib0051 article-title: A reproducing kernel method for solving nonlocal fractional boundary value problems publication-title: Appl. Math. Lett. – volume: 21 start-page: 7191 year: 2017 end-page: 7206 ident: bib0041 article-title: Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems publication-title: Soft Computing – volume: 18 start-page: 1 year: 2016 end-page: 8 ident: bib0025 article-title: A Reliable Algorithm for a Local Fractional Tricomi Equation Arising in Fractal Transonic Flow publication-title: Entropy – volume: 219 start-page: 10225 year: 2013 end-page: 10230 ident: bib0052 article-title: Solving a system of linear Volterra integral equations using the new reproducing kernel method publication-title: Appl. Math. Comput. – volume: 62 start-page: 1127 year: 2011 end-page: 1134 ident: bib0009 article-title: Approximate solution of fractional integro-differential equations by Taylor expansion method publication-title: Computers & Mathematics with Applications – year: 2005 ident: bib0002 article-title: Hamiltonian Chaos and Fractional Dynamics – volume: 146 start-page: 231 year: 2016 end-page: 254 ident: bib0043 article-title: Approximate solutions of DASs with nonclassical boundary conditions using novel reproducing kernel algorithm publication-title: Fundamenta Informaticae – volume: 83 start-page: 2285 year: 2003 end-page: 2286 ident: bib0020 article-title: Fractional signal processing and applications publication-title: Signal Process – start-page: 1 year: 2017 end-page: 12 ident: bib0035 article-title: The RKHS method for numerical treatment for integrodifferential algebraic systems of temporal two-point BVPs publication-title: Neural Computing and Applications – volume: 219 start-page: 8938 year: 2013 end-page: 8948 ident: bib0037 article-title: Solving Fredholm integro-differential equations using reproducing kernel Hilbert space method publication-title: Appl. Math. Comput. – volume: 243 start-page: 911 year: 2014 end-page: 922 ident: bib0038 article-title: Numerical algorithm for solving two-point, second-order periodic boundary value problems for mixed integro-differential equations publication-title: Appl. Math. Comput. – volume: 293 start-page: 81 year: 2015 end-page: 95 ident: bib0018 article-title: Approximate analytical solution of the nonlinear fractional KdV-Burgers equation: A new iterative algorithm publication-title: J. Comput. Phys. – volume: 240 start-page: 229 year: 2014 end-page: 239 ident: bib0039 article-title: A computational method for solving periodic boundary value problems for integro-differential equations of Fredholm-Voltera type publication-title: Appl. Math. Comput. – volume: 255 start-page: 97 year: 2014 end-page: 105 ident: bib0050 article-title: A numerical method for singularly perturbed turning point problems with an interior layer publication-title: J. Comput. Appl. Math. – volume: 230 start-page: 770 year: 2009 end-page: 780 ident: bib0032 article-title: Numerical algorithm for parabolic problems with non-classical conditions publication-title: J. Comput. Appl. Math. – year: 2009 ident: bib0027 article-title: Nonlinear Numerical Analysis in the Reproducing Kernel Space – volume: 16 start-page: 471 year: 2014 end-page: 493 ident: bib0013 article-title: Multiple solutions of nonlinear boundary value problems of fractional order: a new analytic iterative technique publication-title: Entropy – year: 2003 ident: bib0029 article-title: Reproducing Kernel Spaces and Applications – volume: 17 start-page: 20 year: 2015 end-page: 26 ident: bib0024 article-title: Numerical computation of fractional multi-dimensional diffusion equations by using a modified homotopy perturbation method publication-title: Journal of the Association of Arab Universities for Basic and Applied Sciences – volume: 2008 start-page: 1 year: 2008 end-page: 11 ident: bib0033 article-title: Reproducing kernel methods for solving linear initial-boundary-value problems publication-title: Electronic Journal of Differential Equations – volume: 68 start-page: 337 year: 1950 end-page: 404 ident: bib0026 article-title: Theory of reproducing kernels publication-title: Trans. Am. Math. Soc. – volume: 71 start-page: 859 year: 2016 end-page: 868 ident: bib0019 article-title: New exact solutions of nonlinear fractional acoustic wave equations in ultrasound publication-title: Computers & Mathematics with Applications – volume: 29 start-page: 1465 year: 2018 end-page: 1479 ident: bib0044 article-title: Solutions of Bagley-Torvik and Painlevé equations of fractional order using iterative reproducing kernel algorithm publication-title: Neural Computing & Applications – volume: 34 start-page: 1759 year: 2018 end-page: 1780 ident: bib0014 article-title: Solutions of time-fractional Tricomi and Keldysh equations of Dirichlet functions types in Hilbert space publication-title: Numerical Methods for Partial Differential Equations – year: 2004 ident: bib0028 article-title: Reproducing Kernel Hilbert Space in Probability and Statistics – volume: 19 start-page: 808 year: 2006 end-page: 813 ident: bib0031 article-title: Representation of the exact solution for a kind of nonlinear partial differential equations publication-title: Appl. Math. Lett. – reference: A. Kilbas, H. Srivastava, J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, Netherlands, 2006. – volume: 16 start-page: 750 year: 2014 end-page: 762 ident: bib0047 article-title: Analytical solution of nonlinear second-order periodic boundary value problem using reproducing kernel method publication-title: Journal of Computational Analysis and Applications – volume: 14 start-page: 113 year: 2017 ident: bib0008 article-title: Numerical solution of partial integro-differential equations by using projection method publication-title: Mediterranean Journal of Mathematics – volume: 34 start-page: 1577 year: 2018 end-page: 1597 ident: bib0011 article-title: Numerical algorithm for solving time-fractional partial integrodifferential equations subject to initial and Dirichlet boundary conditions publication-title: Numerical Methods for Partial Differential Equations – volume: 73 start-page: 1243 year: 2017 end-page: 1261 ident: bib0034 article-title: Fitted reproducing kernel Hilbert space method for the solutions of some certain classes of time-fractional partial differential equations subject to initial and Neumann boundary conditions publication-title: Computers & Mathematics with Applications – volume: 20 start-page: 3283 year: 2016 end-page: 3302 ident: bib0040 article-title: Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method publication-title: Soft Computing – year: 2014 ident: bib0010 article-title: Numerical solution of fractional integro-differential equations by least squares method and shifted Chebyshev polynomial publication-title: Mathematical Problems in Engineering – volume: 39 start-page: 147 year: 1907 end-page: 196 ident: bib0021 article-title: L'equation biharminique et une class remarquable defonctionsfoundamentals harmoniques publication-title: Bulletin International de l'Academie des Sciences de Cracovie – volume: 39 start-page: 4549 year: 2016 end-page: 4562 ident: bib0036 article-title: The reproducing kernel algorithm for handling differential algebraic systems of ordinary differential equations publication-title: Mathematical Methods in the Applied Sciences – volume: 28 start-page: 828 year: 2018 end-page: 856 ident: bib0045 article-title: Numerical solutions for the Robin time-fractional partial differential equations of heat and fluid flows based on the reproducing kernel algorithm publication-title: International Journal of Numerical Methods for Heat & Fluid Flow – year: 1999 ident: bib0003 article-title: Fractional Differential Equations – year: 2017 ident: bib0046 article-title: Application of reproducing kernel algorithm for solving Dirichlet time-fractional diffusion-Gordon types equations in porous media publication-title: Journal of Porous Media – volume: 257 start-page: 119 year: 2015 end-page: 133 ident: bib0017 article-title: A novel expansion iterative method for solving linear partial differential equations of fractional order publication-title: Appl. Math. Comput. – volume: 39 start-page: 5592 year: 2015 end-page: 5597 ident: bib0053 article-title: Modified reproducing kernel method for singularly perturbed boundary value problems with a delay publication-title: Appl. Math. Modell. – volume: 28 start-page: 1591 year: 2017 end-page: 1610 ident: bib0042 article-title: Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm-Volterra integrodifferential equations publication-title: Neural Computing & Applications – year: 2010 ident: bib0001 article-title: Fractional Calculus and Waves in Linear Viscoelasticity – volume: 28 start-page: 1591 year: 2017 ident: 10.1016/j.amc.2018.09.020_bib0042 article-title: Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm-Volterra integrodifferential equations publication-title: Neural Computing & Applications doi: 10.1007/s00521-015-2110-x – volume: 73 start-page: 1243 year: 2017 ident: 10.1016/j.amc.2018.09.020_bib0034 article-title: Fitted reproducing kernel Hilbert space method for the solutions of some certain classes of time-fractional partial differential equations subject to initial and Neumann boundary conditions publication-title: Computers & Mathematics with Applications doi: 10.1016/j.camwa.2016.11.032 – volume: 68 start-page: 337 year: 1950 ident: 10.1016/j.amc.2018.09.020_bib0026 article-title: Theory of reproducing kernels publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-1950-0051437-7 – year: 2005 ident: 10.1016/j.amc.2018.09.020_bib0002 – volume: 28 start-page: 828 year: 2018 ident: 10.1016/j.amc.2018.09.020_bib0045 article-title: Numerical solutions for the Robin time-fractional partial differential equations of heat and fluid flows based on the reproducing kernel algorithm publication-title: International Journal of Numerical Methods for Heat & Fluid Flow doi: 10.1108/HFF-07-2016-0278 – volume: 257 start-page: 119 year: 2015 ident: 10.1016/j.amc.2018.09.020_bib0017 article-title: A novel expansion iterative method for solving linear partial differential equations of fractional order publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2014.12.121 – volume: 30 start-page: 289 year: 2014 ident: 10.1016/j.amc.2018.09.020_bib0049 article-title: A collocation method based on reproducing kernel for a modified anomalous subdiffusion equation publication-title: Numerical Methods for Partial Differential Equations doi: 10.1002/num.21809 – year: 2014 ident: 10.1016/j.amc.2018.09.020_bib0010 article-title: Numerical solution of fractional integro-differential equations by least squares method and shifted Chebyshev polynomial publication-title: Mathematical Problems in Engineering doi: 10.1155/2014/431965 – volume: 240 start-page: 229 year: 2014 ident: 10.1016/j.amc.2018.09.020_bib0039 article-title: A computational method for solving periodic boundary value problems for integro-differential equations of Fredholm-Voltera type publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2014.04.057 – volume: 26 start-page: 998 year: 2013 ident: 10.1016/j.amc.2018.09.020_bib0048 article-title: Reproducing kernel method for singularly perturbed turning point problems having twin boundary layers publication-title: Appl. Math. Lett. doi: 10.1016/j.aml.2013.05.006 – volume: 146 start-page: 231 year: 2016 ident: 10.1016/j.amc.2018.09.020_bib0043 article-title: Approximate solutions of DASs with nonclassical boundary conditions using novel reproducing kernel algorithm publication-title: Fundamenta Informaticae doi: 10.3233/FI-2016-1384 – volume: 255 start-page: 97 year: 2014 ident: 10.1016/j.amc.2018.09.020_bib0050 article-title: A numerical method for singularly perturbed turning point problems with an interior layer publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2013.04.040 – volume: 293 start-page: 81 year: 2015 ident: 10.1016/j.amc.2018.09.020_bib0018 article-title: Approximate analytical solution of the nonlinear fractional KdV-Burgers equation: A new iterative algorithm publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2014.08.004 – volume: 16 start-page: 750 year: 2014 ident: 10.1016/j.amc.2018.09.020_bib0047 article-title: Analytical solution of nonlinear second-order periodic boundary value problem using reproducing kernel method publication-title: Journal of Computational Analysis and Applications – volume: 34 start-page: 1577 year: 2018 ident: 10.1016/j.amc.2018.09.020_bib0011 article-title: Numerical algorithm for solving time-fractional partial integrodifferential equations subject to initial and Dirichlet boundary conditions publication-title: Numerical Methods for Partial Differential Equations doi: 10.1002/num.22209 – volume: 34 start-page: 1759 year: 2018 ident: 10.1016/j.amc.2018.09.020_bib0014 article-title: Solutions of time-fractional Tricomi and Keldysh equations of Dirichlet functions types in Hilbert space publication-title: Numerical Methods for Partial Differential Equations doi: 10.1002/num.22236 – volume: 21 start-page: 7191 year: 2017 ident: 10.1016/j.amc.2018.09.020_bib0041 article-title: Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems publication-title: Soft Computing doi: 10.1007/s00500-016-2262-3 – volume: 230 start-page: 770 year: 2009 ident: 10.1016/j.amc.2018.09.020_bib0032 article-title: Numerical algorithm for parabolic problems with non-classical conditions publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2009.01.012 – year: 2017 ident: 10.1016/j.amc.2018.09.020_bib0046 article-title: Application of reproducing kernel algorithm for solving Dirichlet time-fractional diffusion-Gordon types equations in porous media publication-title: Journal of Porous Media – year: 2003 ident: 10.1016/j.amc.2018.09.020_bib0029 – volume: 18 start-page: 1 year: 2016 ident: 10.1016/j.amc.2018.09.020_bib0025 article-title: A Reliable Algorithm for a Local Fractional Tricomi Equation Arising in Fractal Transonic Flow publication-title: Entropy doi: 10.3390/e18060206 – volume: 14 start-page: 113 year: 2017 ident: 10.1016/j.amc.2018.09.020_bib0008 article-title: Numerical solution of partial integro-differential equations by using projection method publication-title: Mediterranean Journal of Mathematics doi: 10.1007/s00009-017-0904-z – volume: 2017 start-page: 27 year: 2017 ident: 10.1016/j.amc.2018.09.020_bib0015 article-title: Solving nonlinear Volterra integro-differential equations of fractional order by using Euler wavelet method publication-title: Advances in Difference Equations doi: 10.1186/s13662-017-1085-6 – volume: 83 start-page: 2285 year: 2003 ident: 10.1016/j.amc.2018.09.020_bib0020 article-title: Fractional signal processing and applications publication-title: Signal Process doi: 10.1016/S0165-1684(03)00181-6 – year: 1993 ident: 10.1016/j.amc.2018.09.020_bib0004 – volume: 316 start-page: 504 year: 2018 ident: 10.1016/j.amc.2018.09.020_bib0006 article-title: A fractional epidemiological model for computer viruses pertaining to a new fractional derivative publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2017.08.048 – year: 2010 ident: 10.1016/j.amc.2018.09.020_bib0001 – volume: 219 start-page: 8938 year: 2013 ident: 10.1016/j.amc.2018.09.020_bib0037 article-title: Solving Fredholm integro-differential equations using reproducing kernel Hilbert space method publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2013.03.006 – year: 2013 ident: 10.1016/j.amc.2018.09.020_bib0022 article-title: An Efficient Approach for Fractional Harry Dym Equation by Using Sumudu Transform publication-title: Abstract and Applied Analysis doi: 10.1155/2013/608943 – volume: 17 start-page: 20 year: 2015 ident: 10.1016/j.amc.2018.09.020_bib0024 article-title: Numerical computation of fractional multi-dimensional diffusion equations by using a modified homotopy perturbation method publication-title: Journal of the Association of Arab Universities for Basic and Applied Sciences doi: 10.1016/j.jaubas.2014.02.002 – volume: 25 start-page: 818 year: 2012 ident: 10.1016/j.amc.2018.09.020_bib0051 article-title: A reproducing kernel method for solving nonlocal fractional boundary value problems publication-title: Appl. Math. Lett. doi: 10.1016/j.aml.2011.10.025 – year: 2009 ident: 10.1016/j.amc.2018.09.020_bib0027 – year: 2017 ident: 10.1016/j.amc.2018.09.020_bib0007 article-title: B-spline solution of fractional integro partial differential equation with a weakly singular kernel – year: 2014 ident: 10.1016/j.amc.2018.09.020_bib0012 article-title: Numerical solution of nonlinear fractional Volterra integro-differential equations via Bernoulli polynomials publication-title: Abstract and Applied Analysis doi: 10.1155/2014/162896 – year: 1982 ident: 10.1016/j.amc.2018.09.020_bib0030 article-title: Reproducing Kernel Hilbert Spaces: Applications in Statistical Signal Processing publication-title: Hutchinson Ross – year: 1999 ident: 10.1016/j.amc.2018.09.020_bib0003 – volume: 20 start-page: 3283 year: 2016 ident: 10.1016/j.amc.2018.09.020_bib0040 article-title: Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method publication-title: Soft Computing doi: 10.1007/s00500-015-1707-4 – year: 2004 ident: 10.1016/j.amc.2018.09.020_bib0028 – volume: 71 start-page: 859 year: 2016 ident: 10.1016/j.amc.2018.09.020_bib0019 article-title: New exact solutions of nonlinear fractional acoustic wave equations in ultrasound publication-title: Computers & Mathematics with Applications doi: 10.1016/j.camwa.2016.01.001 – volume: 62 start-page: 1127 year: 2011 ident: 10.1016/j.amc.2018.09.020_bib0009 article-title: Approximate solution of fractional integro-differential equations by Taylor expansion method publication-title: Computers & Mathematics with Applications doi: 10.1016/j.camwa.2011.03.037 – volume: 16 start-page: 471 year: 2014 ident: 10.1016/j.amc.2018.09.020_bib0013 article-title: Multiple solutions of nonlinear boundary value problems of fractional order: a new analytic iterative technique publication-title: Entropy doi: 10.3390/e16010471 – volume: 2008 start-page: 1 year: 2008 ident: 10.1016/j.amc.2018.09.020_bib0033 article-title: Reproducing kernel methods for solving linear initial-boundary-value problems publication-title: Electronic Journal of Differential Equations – volume: 243 start-page: 911 year: 2014 ident: 10.1016/j.amc.2018.09.020_bib0038 article-title: Numerical algorithm for solving two-point, second-order periodic boundary value problems for mixed integro-differential equations publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2014.06.063 – volume: 39 start-page: 5592 year: 2015 ident: 10.1016/j.amc.2018.09.020_bib0053 article-title: Modified reproducing kernel method for singularly perturbed boundary value problems with a delay publication-title: Appl. Math. Modell. doi: 10.1016/j.apm.2015.01.021 – volume: 39 start-page: 4549 year: 2016 ident: 10.1016/j.amc.2018.09.020_bib0036 article-title: The reproducing kernel algorithm for handling differential algebraic systems of ordinary differential equations publication-title: Mathematical Methods in the Applied Sciences doi: 10.1002/mma.3884 – start-page: 1 year: 2017 ident: 10.1016/j.amc.2018.09.020_bib0035 article-title: The RKHS method for numerical treatment for integrodifferential algebraic systems of temporal two-point BVPs publication-title: Neural Computing and Applications – ident: 10.1016/j.amc.2018.09.020_bib0005 – volume: 29 start-page: 1465 year: 2018 ident: 10.1016/j.amc.2018.09.020_bib0044 article-title: Solutions of Bagley-Torvik and Painlevé equations of fractional order using iterative reproducing kernel algorithm publication-title: Neural Computing & Applications doi: 10.1007/s00521-016-2484-4 – volume: 39 start-page: 147 year: 1907 ident: 10.1016/j.amc.2018.09.020_bib0021 article-title: L'equation biharminique et une class remarquable defonctionsfoundamentals harmoniques publication-title: Bulletin International de l'Academie des Sciences de Cracovie – volume: 293 start-page: 385 year: 2015 ident: 10.1016/j.amc.2018.09.020_bib0016 article-title: Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2014.09.034 – start-page: 1 year: 2017 ident: 10.1016/j.amc.2018.09.020_bib0023 article-title: An efficient computational approach for time-fractional Rosenau–Hyman equation publication-title: Neural Computing and Applications – volume: 219 start-page: 10225 year: 2013 ident: 10.1016/j.amc.2018.09.020_bib0052 article-title: Solving a system of linear Volterra integral equations using the new reproducing kernel method publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2013.03.123 – volume: 19 start-page: 808 year: 2006 ident: 10.1016/j.amc.2018.09.020_bib0031 article-title: Representation of the exact solution for a kind of nonlinear partial differential equations publication-title: Appl. Math. Lett. doi: 10.1016/j.aml.2005.10.010 |
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