Computational algorithm for solving singular Fredholm time-fractional partial integrodifferential equations with error estimates

In this article, we propose and analyze an efficient computational algorithm for the numerical solutions of singular Fredholm time-fractional partial integrodifferential equations subject to Dirichlet functions type. The algorithm provide appropriate representation of the solutions in infinite serie...

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Vydané v:	Journal of applied mathematics & computing Ročník 59; číslo 1-2; s. 227 - 243
Hlavný autor:	Abu Arqub, Omar
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Berlin/Heidelberg Springer Berlin Heidelberg 15.02.2019 Springer Nature B.V
Predmet:	Algorithms Applied mathematics Computational Mathematics and Numerical Analysis Computer simulation Dirichlet problem Error analysis Infinite series Mathematical and Computational Engineering Mathematics Mathematics and Statistics Mathematics of Computing Nonlinear equations Original Research Simulated annealing Theory of Computation Fredholm operator Reproducing kernel algorithm Fractional calculus theory Singular partial integrodifferential equation
ISSN:	1598-5865, 1865-2085
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Abstract	In this article, we propose and analyze an efficient computational algorithm for the numerical solutions of singular Fredholm time-fractional partial integrodifferential equations subject to Dirichlet functions type. The algorithm provide appropriate representation of the solutions in infinite series formula with accurately computable structures. By interrupting the n -term of exact solutions, numerical solutions of linear and nonlinear time-fractional equations of nonhomogeneous function type are studied from mathematical viewpoint. Convergence analysis, error estimations, and error bounds under some hypotheses which provide the theoretical basis of the proposed algorithm are also discussed. The dynamical properties of these numerical solutions are discussed and the profiles of several representative numerical solutions are illustrated. Finally, the utilized results show that the present algorithm and simulated annealing provide a good scheduling methodology to such integrodifferential equations.
AbstractList	In this article, we propose and analyze an efficient computational algorithm for the numerical solutions of singular Fredholm time-fractional partial integrodifferential equations subject to Dirichlet functions type. The algorithm provide appropriate representation of the solutions in infinite series formula with accurately computable structures. By interrupting the n-term of exact solutions, numerical solutions of linear and nonlinear time-fractional equations of nonhomogeneous function type are studied from mathematical viewpoint. Convergence analysis, error estimations, and error bounds under some hypotheses which provide the theoretical basis of the proposed algorithm are also discussed. The dynamical properties of these numerical solutions are discussed and the profiles of several representative numerical solutions are illustrated. Finally, the utilized results show that the present algorithm and simulated annealing provide a good scheduling methodology to such integrodifferential equations. In this article, we propose and analyze an efficient computational algorithm for the numerical solutions of singular Fredholm time-fractional partial integrodifferential equations subject to Dirichlet functions type. The algorithm provide appropriate representation of the solutions in infinite series formula with accurately computable structures. By interrupting the n -term of exact solutions, numerical solutions of linear and nonlinear time-fractional equations of nonhomogeneous function type are studied from mathematical viewpoint. Convergence analysis, error estimations, and error bounds under some hypotheses which provide the theoretical basis of the proposed algorithm are also discussed. The dynamical properties of these numerical solutions are discussed and the profiles of several representative numerical solutions are illustrated. Finally, the utilized results show that the present algorithm and simulated annealing provide a good scheduling methodology to such integrodifferential equations.
Author	Abu Arqub, Omar
Author_xml	– sequence: 1 givenname: Omar orcidid: 0000-0001-9526-6095 surname: Abu Arqub fullname: Abu Arqub, Omar email: o.abuarqub@bau.edu.jo organization: Department of Mathematics, Faculty of Science, Al-Balqa Applied University
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Copyright	Korean Society for Computational and Applied Mathematics 2018 Journal of Applied Mathematics and Computing is a copyright of Springer, (2018). All Rights Reserved.
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Snippet	In this article, we propose and analyze an efficient computational algorithm for the numerical solutions of singular Fredholm time-fractional partial...
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SubjectTerms	Algorithms Applied mathematics Computational Mathematics and Numerical Analysis Computer simulation Dirichlet problem Error analysis Infinite series Mathematical and Computational Engineering Mathematics Mathematics and Statistics Mathematics of Computing Nonlinear equations Original Research Simulated annealing Theory of Computation
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Title	Computational algorithm for solving singular Fredholm time-fractional partial integrodifferential equations with error estimates
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