Numerical analysis of nonlinear fractional Klein–Fock–Gordon equation arising in quantum field theory via Caputo–Fabrizio fractional operator
The present article deals with the solution of nonlinear fractional Klein–Fock–Gordon equation which involved the newly developed Caputo–Fabrizio fractional derivative with non-singular kernel. We adopt fractional homotopy perturbation transform method in order to find the approximate solution of fr...
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| Published in: | Mathematical sciences (Karaj, Iran) Vol. 15; no. 3; pp. 269 - 281 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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Berlin/Heidelberg
Springer Berlin Heidelberg
01.09.2021
Springer Nature B.V |
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| ISSN: | 2008-1359, 2251-7456 |
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| Abstract | The present article deals with the solution of nonlinear fractional Klein–Fock–Gordon equation which involved the newly developed Caputo–Fabrizio fractional derivative with non-singular kernel. We adopt fractional homotopy perturbation transform method in order to find the approximate solution of fractional Klein–Fock–Gordon equation in the form of rapidly convergent series. Existence and uniqueness analysis of the considered model is provided. We consider few numerical examples to validate the projected technique. The obtained results shows that this method is very efficient, simple in implementation and that it can be applied to solve other nonlinear problems. |
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| AbstractList | The present article deals with the solution of nonlinear fractional Klein–Fock–Gordon equation which involved the newly developed Caputo–Fabrizio fractional derivative with non-singular kernel. We adopt fractional homotopy perturbation transform method in order to find the approximate solution of fractional Klein–Fock–Gordon equation in the form of rapidly convergent series. Existence and uniqueness analysis of the considered model is provided. We consider few numerical examples to validate the projected technique. The obtained results shows that this method is very efficient, simple in implementation and that it can be applied to solve other nonlinear problems. |
| Author | Prakash, Amit Kumar, Ashok Baskonus, Haci Mehmet Kumar, Ajay |
| Author_xml | – sequence: 1 givenname: Amit orcidid: 0000-0003-0963-4651 surname: Prakash fullname: Prakash, Amit email: amitmath@nitkkr.ac.in organization: Department of Mathematics, National Institute of Technology – sequence: 2 givenname: Ajay surname: Kumar fullname: Kumar, Ajay organization: Department of Mathematics, H. N. B. Garhwal University (A Central University) – sequence: 3 givenname: Haci Mehmet surname: Baskonus fullname: Baskonus, Haci Mehmet organization: Department of Mathematics and Science Education, Faculty of Education, Harran University – sequence: 4 givenname: Ashok surname: Kumar fullname: Kumar, Ashok organization: Department of Mathematics, H. N. B. Garhwal University (A Central University) |
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| Cites_doi | 10.1002/mma.6886 10.1142/S0217979220502264 10.1142/S0217979220501490 10.1108/ec-02-2020-0091 10.1002/num.22476 10.3390/math8060908 10.1016/j.jppr.2018.07.005 10.1515/phys-2016-0021 10.1016/j.joes.2019.06.001 10.3844/jmssp.2016.23.33 10.1016/j.chaos.2005.08.178 10.1016/j.aej.2015.05.004 10.1016/S0045-7825(99)00018-3 10.1016/j.chaos.2016.03.026 10.3934/math.2020068 10.1016/j.aej.2014.02.001 10.1016/j.amc.2019.124637 10.1016/j.camwa.2010.10.045 10.1016/j.matcom.2020.09.016 10.1016/j.amc.2013.07.088 10.1016/j.aej.2019.12.022 10.1016/j.physleta.2005.10.099 10.1142/S0217979219503508 10.3390/math8030341 10.1016/S0375-9601(00)00330-3 10.1016/j.chaos.2007.02.012 10.1016/j.cnsns.2013.10.001 10.1016/j.matcom.2019.10.010 10.1016/j.aml.2007.07.023 10.1016/j.camwa.2011.03.057 10.1016/j.aml.2013.05.010 10.1016/j.camwa.2010.08.022 10.1007/s40009-013-0209-0 10.1016/j.physleta.2007.01.046 10.1016/j.aej.2020.05.007 10.1016/j.amc.2015.03.037 10.1016/j.aej.2020.02.008 10.1016/j.jde.2004.07.026 10.1016/j.chaos.2020.110096 10.1016/j.cpc.2008.11.012 10.1016/j.aej.2020.01.032 10.1515/nleng-2018-0001 |
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| Keywords | Caputo–Fabrizio fractional operator Fractional Klein–Fock–Gordon equation Laplace transform Fractional Homotopy perturbation transform method |
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| References | Podlubny (CR57) 1999 Guirao, Baskonus, Kumar (CR11) 2020; 8 Craddock, Platen (CR38) 2004; 207 Yusufoglu (CR45) 2008; 21 Prakash, Kumar (CR27) 2019; 9 Aruna, Ravi Kanth (CR48) 2014; 37 Fainberg, Pimentel (CR55) 2000; 271 He (CR28) 1999; 178 Yokus, Durur, Ahmad, Yao (CR42) 2020; 8 Goyal, Baskonus, Prakash (CR20) 2020; 139 Gupta, Singh (CR30) 2011; 61 Yokus, Kuzu, Demiroglu (CR41) 2019; 33 Veeresha, Prakasha, Kumar (CR50) 2020; 364 Caputo (CR56) 1969 Saelao, Yokchoo (CR35) 2020; 171 Shirkhani, Hoshyara, Rahimipetroudi, Akhavan, Ganji (CR8) 2018; 7 Yokus (CR40) 2020; 2050149 Algahtani (CR31) 2016; 89 Gong, Khan (CR33) 2020; 59 Kochetov (CR53) 2014; 19 Assas (CR18) 2008; 38 Ravi Kanth, Aruna (CR47) 2009; 180 Yépez-Martínez, Gómez-Aguilar (CR34) 2020; 346 Guirao, Baskonus, Kumar, Rawat, Yel (CR9) 2020; 12 Verma, Prakash, Kumar, Singh (CR23) 2019; 4 Gupta (CR13) 2011; 61 Momani, Odibat (CR29) 2007; 365 Prakash, Kumar (CR21) 2016; 14 Khan, Wu (CR1) 2011; 61 Gupta, Kumar, Singh (CR2) 2015; 54 Kumar, Singh, Kumar (CR49) 2014; 53 Yavuz, Yokus (CR44) 2020; 5 Zhenga, Wanga, Fu (CR32) 2020; 138 Prakash, Goyal, Gupta (CR17) 2019; 8 Baskonus, Kumar, Gao (CR12) 2020; 2050152 Jleli, Kumar, Kumar, Samet (CR4) 2020; 59 Prakash, Verma (CR15) 2020 Padmavathi, Prakash, Alagesan, Magesh (CR26) 2020 Singh, Kumar, Singh, Singh (CR51) 2019; 67 Aero, Bulygin, Pavlov (CR54) 2013; 223 Chen, Tian, Qu, Li, Zhao, Tian, Wang (CR43) 2020; 2050226 Khan, Rasheed (CR46) 2015; 4 Prakash, Goyal, Baskonus, Gupta (CR14) 2020; 5 Abuteen, Freihat, Al-Smadi, Khalil, Khan (CR52) 2016; 12 Prakash, Kaur (CR3) 2021; 181 Baleanu, Aydogn, Mohammadi, Rezapour (CR36) 2020; 59 Golshan, Nourazar, Fard, Yildirim, Campo (CR7) 2013; 26 Prakash (CR6) 2016; 5 Abbasbandy (CR5) 2006; 30 Prakash, Kumar, Sharma (CR22) 2015; 260 Prakash, Kaur (CR25) 2018; 9 Prakash, Verma (CR24) 2019; 93 Gupta, Goyal, Prakash (CR19) 2020; 10 Yokus, Durur, Ahmad, Thounthong, Zhang (CR39) 2020; 103409 Diethelm (CR58) 2004 Zhang, Wang, Feng (CR37) 2006; 350 Guirao, Baskonus, Kumar, Causanilles, Bermudez (CR10) 2020; 59 Goyal, Baskonus, Prakash (CR16) 2019; 134 Caputo, Fabrizio (CR59) 2015; 1 A Prakash (365_CR22) 2015; 260 PK Gupta (365_CR30) 2011; 61 Y Chen (365_CR43) 2020; 2050226 H Singh (365_CR51) 2019; 67 JLG Guirao (365_CR10) 2020; 59 A Yokus (365_CR42) 2020; 8 Y Khan (365_CR1) 2011; 61 NA Khan (365_CR46) 2015; 4 A Prakash (365_CR24) 2019; 93 M Craddock (365_CR38) 2004; 207 A Yokus (365_CR41) 2019; 33 M Yavuz (365_CR44) 2020; 5 S Gupta (365_CR19) 2020; 10 S Abbasbandy (365_CR5) 2006; 30 OJJ Algahtani (365_CR31) 2016; 89 E Yusufoglu (365_CR45) 2008; 21 K Diethelm (365_CR58) 2004 JLG Guirao (365_CR9) 2020; 12 HM Baskonus (365_CR12) 2020; 2050152 M Jleli (365_CR4) 2020; 59 A Prakash (365_CR14) 2020; 5 M Caputo (365_CR59) 2015; 1 E Abuteen (365_CR52) 2016; 12 A Prakash (365_CR25) 2018; 9 D Baleanu (365_CR36) 2020; 59 X Gong (365_CR33) 2020; 59 H Yépez-Martínez (365_CR34) 2020; 346 A Yokus (365_CR40) 2020; 2050149 A Prakash (365_CR3) 2021; 181 S Gupta (365_CR2) 2015; 54 A Prakash (365_CR6) 2016; 5 PK Gupta (365_CR13) 2011; 61 JL Zhang (365_CR37) 2006; 350 JLG Guirao (365_CR11) 2020; 8 A Prakash (365_CR17) 2019; 8 A Prakash (365_CR15) 2020 EL Aero (365_CR54) 2013; 223 ASV Ravi Kanth (365_CR47) 2009; 180 AN Golshan (365_CR7) 2013; 26 M Caputo (365_CR56) 1969 V Verma (365_CR23) 2019; 4 BA Kochetov (365_CR53) 2014; 19 M Goyal (365_CR16) 2019; 134 D Kumar (365_CR49) 2014; 53 J Saelao (365_CR35) 2020; 171 A Yokus (365_CR39) 2020; 103409 X Zhenga (365_CR32) 2020; 138 S Momani (365_CR29) 2007; 365 JH He (365_CR28) 1999; 178 MR Shirkhani (365_CR8) 2018; 7 LMB Assas (365_CR18) 2008; 38 V Padmavathi (365_CR26) 2020 K Aruna (365_CR48) 2014; 37 A Prakash (365_CR27) 2019; 9 A Prakash (365_CR21) 2016; 14 VY Fainberg (365_CR55) 2000; 271 I Podlubny (365_CR57) 1999 P Veeresha (365_CR50) 2020; 364 M Goyal (365_CR20) 2020; 139 |
| References_xml | – volume: 59 start-page: 2859 issue: 5 year: 2020 end-page: 2863 ident: CR4 article-title: Analytical approach for time fractional wave equations in the sense of Yang–Abdel-Aty–Cattani via the homotopy perturbation transform method publication-title: Alex. Eng. J. – volume: 67 start-page: 21 issue: 1 year: 2019 end-page: 34 ident: CR51 article-title: A reliable numerical algorithm for the fractional Klein–Gordon equation publication-title: Eng. Trans. – volume: 33 start-page: 1 issue: 29 year: 2019 end-page: 19 ident: CR41 article-title: Investigation of solitary wave solutions for the (3 + 1)-dimensional Zakharov–Kuznetsov equation publication-title: Int. J. Mod. Phys. B – volume: 181 start-page: 298 year: 2021 end-page: 315 ident: CR3 article-title: Analysis and numerical simulation of fractional Biswas–Milovic model publication-title: Math. Comput. Simul. – volume: 61 start-page: 250 issue: 2 year: 2011 end-page: 254 ident: CR30 article-title: Homotopy perturbation method for fractional Fornberg–Whitham equation publication-title: Comput. Math Appl. – volume: 207 start-page: 285 issue: 2 year: 2004 end-page: 302 ident: CR38 article-title: Symmetry group methods for fundamental solutions publication-title: J. Differ. Equ. – volume: 37 start-page: 163 issue: 2 year: 2014 end-page: 171 ident: CR48 article-title: Two-dimensional differential transform method and modified differential transform method for solving nonlinear fractional Klein–Gordon equation publication-title: Nat. Acad. Sci. Lett. – volume: 5 start-page: 979 issue: 2 year: 2020 end-page: 1000 ident: CR14 article-title: A reliable hybrid numerical method for a time-dependent vibration model of arbitrary order publication-title: AIMS Math. – volume: 4 start-page: 338 year: 2019 end-page: 351 ident: CR23 article-title: Numerical study of fractional model of multi-dimensional dispersive partial differential equation publication-title: J. Ocean Eng. Sci. – volume: 271 start-page: 16 year: 2000 end-page: 25 ident: CR55 article-title: Duffin–Kemmer–Petiau and Klein–Gordon–Fock equations for electromagnetic, Yang–Mills and external gravitational field interactions: proof of equivalence publication-title: Phys. Lett. A – volume: 4 start-page: 43 issue: 1 year: 2015 end-page: 48 ident: CR46 article-title: Analytical solutions of linear and nonlinear Klein–Fock–Gordon equation publication-title: Nonlinear Eng.-Model. Appl. – volume: 8 start-page: 164 year: 2019 end-page: 171 ident: CR17 article-title: Fractional variational iteration method for solving time-fractional Newell–Whitehead–Segel equation publication-title: Nonlinear Eng.-Model. Appl. – volume: 7 start-page: 247 issue: 3 year: 2018 end-page: 256 ident: CR8 article-title: Unsteady time dependent incompressible Newtonian fluid flow between two parallel plates by homotopy analysis method (HAM), homotopy perturbation method (HPM) and collocation method (CM) publication-title: Propuls. Power Res. – volume: 61 start-page: 2829 issue: 9 year: 2011 end-page: 2842 ident: CR13 article-title: Approximate analytical solutions of fractional Benney-Lin equation by reduced differential transform method and the homotopy perturbation method publication-title: Comput. Math Appl. – volume: 139 start-page: 1 year: 2020 end-page: 12 ident: CR20 article-title: Regarding new positive, bounded and convergent numerical solution of nonlinear time fractional HIV/AIDS transmission model publication-title: Chaos Solitons Fract. – volume: 14 start-page: 177 year: 2016 end-page: 186 ident: CR21 article-title: Numerical solution of two-dimensional time fractional order biological population model publication-title: Open Phys. – volume: 93 start-page: 1 issue: 66 year: 2019 end-page: 19 ident: CR24 article-title: Numerical solution of nonlinear fractional Zakharov–Kuznetsov equation arising in ion-acoustic waves publication-title: Pramana-J. Phys. – volume: 59 start-page: 2251 issue: 4 year: 2020 end-page: 2259 ident: CR33 article-title: A new numerical solution of the competition model among bank data in Caputo–Fabrizio derivative publication-title: Alex. Eng. J. – volume: 12 start-page: 1 issue: 17 year: 2020 end-page: 10 ident: CR9 article-title: Complex patterns to the (3 + 1)-dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation publication-title: Symmetry. – volume: 10 start-page: 312 issue: 2 year: 2020 end-page: 320 ident: CR19 article-title: Numerical treatment of Newell–Whitehead–Segel equation publication-title: TWMS J. App. Eng. Math. – volume: 103409 start-page: 1 issue: 19 year: 2020 end-page: 8 ident: CR39 article-title: Construction of exact traveling wave solutions of the Bogoyavlenskii equation by (G′/G, 1/G)-expansion and (1/G′)-expansion techniques publication-title: Results Phys. – volume: 260 start-page: 314 year: 2015 end-page: 320 ident: CR22 article-title: Numerical method for solving coupled Burgers equation publication-title: Appl. Math. Comput. – volume: 171 start-page: 94 year: 2020 end-page: 102 ident: CR35 article-title: The solution of Klein–Gordon equation by using modified Adomian decomposition method publication-title: Math. Comput. Simul. – volume: 346 start-page: 247 issue: 15 year: 2020 end-page: 260 ident: CR34 article-title: A new modified definition of Caputo–Fabrizio fractional order derivative and their applications to the multi-step homotopy analysis method publication-title: J. Comput. Appl. Math. – volume: 59 start-page: 3029 issue: 5 year: 2020 end-page: 3039 ident: CR36 article-title: On modelling of epidemic childhood diseases with the Caputo–Fabrizio derivative by using the Laplace Adomian decomposition method publication-title: Alex. Eng. J. – year: 2004 ident: CR58 publication-title: The Analysis of Fractional Differential Equations – volume: 178 start-page: 257 issue: 3–4 year: 1999 end-page: 262 ident: CR28 article-title: Homotopy perturbation technique publication-title: Comput. Methods Appl. Mech. Eng. – volume: 223 start-page: 160 issue: 15 year: 2013 end-page: 166 ident: CR54 article-title: Functionally invariant solutions of nonlinear Klein–Fock–Gordon equation publication-title: Appl. Math. Comput. – volume: 26 start-page: 1018 issue: 10 year: 2013 end-page: 1025 ident: CR7 article-title: A modified homotopy perturbation method coupled with the Fourier transform for nonlinear and singular Lane–Emden equations publication-title: Appl. Math. Lett. – volume: 59 start-page: 2149 issue: 4 year: 2020 end-page: 2160 ident: CR10 article-title: Complex mixed dark bright wave patterns to the modified and modified Vakhnenko–Parkes equations publication-title: Alex. Eng. J. – volume: 8 start-page: 341 issue: 3 year: 2020 ident: CR11 article-title: Regarding new wave patterns of the newly extended nonlinear (2 + 1)-dimensional Boussinesq equation with fourth order publication-title: Mathematics. – volume: 180 start-page: 708 year: 2009 end-page: 711 ident: CR47 article-title: Differential transform method for solving the linear and nonlinear Klein–Gordon equation publication-title: Comput. Phys. Commun. – volume: 30 start-page: 1206 year: 2006 end-page: 1212 ident: CR5 article-title: Application of He’s homotopy perturbation method for Laplace transform publication-title: Chaos Solitons Fract. – volume: 5 start-page: 123 issue: 2 year: 2016 end-page: 128 ident: CR6 article-title: Analytical method for space-fractional telegraph equation by Homotopy perturbation transform method publication-title: Nonlinear Eng.-Model. Appl. – volume: 9 start-page: 446 issue: 3 year: 2019 end-page: 454 ident: CR27 article-title: Numerical solution of time-fractional order Fokker–Planck equation publication-title: TWMS J. App. Eng. Math. – year: 2020 ident: CR26 article-title: Analysis and numerical simulation of novel coronavirus (COVID-19) model with Mittag–Leffler Kernel publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.6886 – volume: 2050226 start-page: 1 year: 2020 end-page: 8 ident: CR43 article-title: Ablowitz–Kaup Newell–Segur system, conservation laws and Backlund transformation of a variable-coefficient Korteweg-de Vries equation in plasma physics, fluid dynamics or atmospheric science publication-title: Int. J. Mod. Phys. B doi: 10.1142/S0217979220502264 – volume: 38 start-page: 1225 issue: 4 year: 2008 end-page: 1228 ident: CR18 article-title: Variational iteration method for solving coupled-KdV equations publication-title: Chaos Solitons Fract. – volume: 89 start-page: 552 year: 2016 end-page: 559 ident: CR31 article-title: Comparing the Atangana–Baleanu and Caputo–Fabrizio derivative with fractional order: Allen Cahn model publication-title: Chaos Solitons Fract. – volume: 12 start-page: 23 issue: 1 year: 2016 end-page: 33 ident: CR52 article-title: Approximate series solution of nonlinear fractional Klein–Gordon equations using fractional reduced differential transform method publication-title: J. Math. Stat. – volume: 2050149 start-page: 1 year: 2020 end-page: 12 ident: CR40 article-title: On the exact and numerical solutions to the FitzHugh-Nagumo equation publication-title: Int. J. Mod. Phys. B doi: 10.1142/S0217979220501490 – volume: 2050152 start-page: 1 year: 2020 end-page: 16 ident: CR12 article-title: Deeper investigations of the (4 + 1)-dimensional Fokas and (2 + 1)-dimensional Breaking soliton equations publication-title: Int. J. Mod. Phys. B – volume: 19 start-page: 1723 issue: 6 year: 2014 end-page: 1728 ident: CR53 article-title: Lie group symmetries and Riemann function of Klein–Gordon–Fock equation with central symmetry publication-title: Commun. Nonlinear Sci. Numer. Simul. – year: 1969 ident: CR56 publication-title: Elasticita e Dissipazione – volume: 53 start-page: 469 year: 2014 end-page: 474 ident: CR49 article-title: Numerical computation of Klein–Gordon equations arising in quantum field theory by using homotopy analysis transform method publication-title: Alex. Eng. J. – volume: 134 start-page: 1 issue: 482 year: 2019 end-page: 10 ident: CR16 article-title: An efficient technique for a time fractional model of lassa hemorrhagic fever spreading in pregnant women publication-title: Eur. Phys. J. Plus. – volume: 365 start-page: 345 issue: 5–6 year: 2007 end-page: 350 ident: CR29 article-title: Homotopy perturbation method for nonlinear partial differential equations of fractional order publication-title: Phys. Lett. A – volume: 364 start-page: 124637 issue: 1 year: 2020 ident: CR50 article-title: An efficient technique for nonlinear time-fractional Klein–Fock–Gordon equation publication-title: Appl. Math. Comput. – year: 1999 ident: CR57 publication-title: Fractional Differential Equations – year: 2020 ident: CR15 article-title: Two efficient computational technique for fractional nonlinear Hirota–Satsuma coupled KdV equations publication-title: Eng. Comput. doi: 10.1108/ec-02-2020-0091 – volume: 350 start-page: 103 issue: 1–2 year: 2006 end-page: 109 ident: CR37 article-title: The improved F-expansion method and its applications publication-title: Phys. Lett. A – volume: 61 start-page: 1963 issue: 8 year: 2011 end-page: 1967 ident: CR1 article-title: Homotopy perturbation transform method for nonlinear equations using He’s polynomials publication-title: Comput. Math Appl. – volume: 54 start-page: 645 issue: 3 year: 2015 end-page: 651 ident: CR2 article-title: Analytical solutions of convection-diffusion problems by combining Laplace transform method and homotopy perturbation method publication-title: Alex. Eng. J. – volume: 9 start-page: 44 issue: 1 year: 2018 end-page: 61 ident: CR25 article-title: q-homotopy analysis transform method for space and time-fractional KdV-Burgers equation publication-title: Nonlinear Sci. Lett. A. – volume: 21 start-page: 669 year: 2008 end-page: 674 ident: CR45 article-title: The variational iteration method for studying the Klein–Gordon equation publication-title: Appl. Math. Lett. – volume: 5 start-page: 1 year: 2020 end-page: 21 ident: CR44 article-title: Analytical and numerical approaches to nerve impulse model of fractional-order publication-title: Numer Methods Partial Differ. Equ. doi: 10.1002/num.22476 – volume: 138 start-page: 1 issue: 109966 year: 2020 end-page: 7 ident: CR32 article-title: Well-posedness of fractional differential equations with variable-order Caputo–Fabrizio derivative publication-title: Chaos Solitons Fract. – volume: 8 start-page: 1 issue: 908 year: 2020 end-page: 16 ident: CR42 article-title: Construction of different types analytic solutions for the Zhiber–Shabat equation publication-title: Mathematics. doi: 10.3390/math8060908 – volume: 1 start-page: 73 year: 2015 end-page: 85 ident: CR59 article-title: A new definition of fractional derivative without singular kernel publication-title: Prog. Fract. Differ. Appl. – volume: 103409 start-page: 1 issue: 19 year: 2020 ident: 365_CR39 publication-title: Results Phys. – volume: 7 start-page: 247 issue: 3 year: 2018 ident: 365_CR8 publication-title: Propuls. Power Res. doi: 10.1016/j.jppr.2018.07.005 – volume: 9 start-page: 44 issue: 1 year: 2018 ident: 365_CR25 publication-title: Nonlinear Sci. Lett. A. – volume: 5 start-page: 1 year: 2020 ident: 365_CR44 publication-title: Numer Methods Partial Differ. Equ. doi: 10.1002/num.22476 – volume: 14 start-page: 177 year: 2016 ident: 365_CR21 publication-title: Open Phys. doi: 10.1515/phys-2016-0021 – volume: 4 start-page: 43 issue: 1 year: 2015 ident: 365_CR46 publication-title: Nonlinear Eng.-Model. Appl. – volume: 4 start-page: 338 year: 2019 ident: 365_CR23 publication-title: J. Ocean Eng. Sci. doi: 10.1016/j.joes.2019.06.001 – volume: 138 start-page: 1 issue: 109966 year: 2020 ident: 365_CR32 publication-title: Chaos Solitons Fract. – volume: 2050152 start-page: 1 year: 2020 ident: 365_CR12 publication-title: Int. J. Mod. Phys. B – volume: 67 start-page: 21 issue: 1 year: 2019 ident: 365_CR51 publication-title: Eng. Trans. – volume: 12 start-page: 23 issue: 1 year: 2016 ident: 365_CR52 publication-title: J. Math. Stat. doi: 10.3844/jmssp.2016.23.33 – volume: 30 start-page: 1206 year: 2006 ident: 365_CR5 publication-title: Chaos Solitons Fract. doi: 10.1016/j.chaos.2005.08.178 – volume: 54 start-page: 645 issue: 3 year: 2015 ident: 365_CR2 publication-title: Alex. Eng. J. doi: 10.1016/j.aej.2015.05.004 – volume: 178 start-page: 257 issue: 3–4 year: 1999 ident: 365_CR28 publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/S0045-7825(99)00018-3 – year: 2020 ident: 365_CR26 publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.6886 – volume: 9 start-page: 446 issue: 3 year: 2019 ident: 365_CR27 publication-title: TWMS J. App. Eng. Math. – volume: 89 start-page: 552 year: 2016 ident: 365_CR31 publication-title: Chaos Solitons Fract. doi: 10.1016/j.chaos.2016.03.026 – volume: 5 start-page: 979 issue: 2 year: 2020 ident: 365_CR14 publication-title: AIMS Math. doi: 10.3934/math.2020068 – volume: 53 start-page: 469 year: 2014 ident: 365_CR49 publication-title: Alex. Eng. J. doi: 10.1016/j.aej.2014.02.001 – volume: 364 start-page: 124637 issue: 1 year: 2020 ident: 365_CR50 publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2019.124637 – volume: 61 start-page: 250 issue: 2 year: 2011 ident: 365_CR30 publication-title: Comput. Math Appl. doi: 10.1016/j.camwa.2010.10.045 – volume-title: Fractional Differential Equations year: 1999 ident: 365_CR57 – volume: 181 start-page: 298 year: 2021 ident: 365_CR3 publication-title: Math. Comput. Simul. doi: 10.1016/j.matcom.2020.09.016 – volume: 223 start-page: 160 issue: 15 year: 2013 ident: 365_CR54 publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2013.07.088 – volume: 59 start-page: 2859 issue: 5 year: 2020 ident: 365_CR4 publication-title: Alex. Eng. J. doi: 10.1016/j.aej.2019.12.022 – volume: 350 start-page: 103 issue: 1–2 year: 2006 ident: 365_CR37 publication-title: Phys. Lett. A doi: 10.1016/j.physleta.2005.10.099 – volume: 33 start-page: 1 issue: 29 year: 2019 ident: 365_CR41 publication-title: Int. J. Mod. Phys. B doi: 10.1142/S0217979219503508 – volume-title: The Analysis of Fractional Differential Equations year: 2004 ident: 365_CR58 – volume: 8 start-page: 1 issue: 908 year: 2020 ident: 365_CR42 publication-title: Mathematics. doi: 10.3390/math8060908 – volume: 8 start-page: 341 issue: 3 year: 2020 ident: 365_CR11 publication-title: Mathematics. doi: 10.3390/math8030341 – volume-title: Elasticita e Dissipazione year: 1969 ident: 365_CR56 – volume: 271 start-page: 16 year: 2000 ident: 365_CR55 publication-title: Phys. Lett. A doi: 10.1016/S0375-9601(00)00330-3 – volume: 38 start-page: 1225 issue: 4 year: 2008 ident: 365_CR18 publication-title: Chaos Solitons Fract. doi: 10.1016/j.chaos.2007.02.012 – volume: 19 start-page: 1723 issue: 6 year: 2014 ident: 365_CR53 publication-title: Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2013.10.001 – volume: 2050226 start-page: 1 year: 2020 ident: 365_CR43 publication-title: Int. J. Mod. Phys. B doi: 10.1142/S0217979220502264 – volume: 171 start-page: 94 year: 2020 ident: 365_CR35 publication-title: Math. Comput. Simul. doi: 10.1016/j.matcom.2019.10.010 – year: 2020 ident: 365_CR15 publication-title: Eng. Comput. doi: 10.1108/ec-02-2020-0091 – volume: 10 start-page: 312 issue: 2 year: 2020 ident: 365_CR19 publication-title: TWMS J. App. Eng. Math. – volume: 21 start-page: 669 year: 2008 ident: 365_CR45 publication-title: Appl. Math. Lett. doi: 10.1016/j.aml.2007.07.023 – volume: 61 start-page: 2829 issue: 9 year: 2011 ident: 365_CR13 publication-title: Comput. Math Appl. doi: 10.1016/j.camwa.2011.03.057 – volume: 26 start-page: 1018 issue: 10 year: 2013 ident: 365_CR7 publication-title: Appl. Math. Lett. doi: 10.1016/j.aml.2013.05.010 – volume: 134 start-page: 1 issue: 482 year: 2019 ident: 365_CR16 publication-title: Eur. Phys. J. Plus. – volume: 61 start-page: 1963 issue: 8 year: 2011 ident: 365_CR1 publication-title: Comput. Math Appl. doi: 10.1016/j.camwa.2010.08.022 – volume: 37 start-page: 163 issue: 2 year: 2014 ident: 365_CR48 publication-title: Nat. Acad. Sci. Lett. doi: 10.1007/s40009-013-0209-0 – volume: 93 start-page: 1 issue: 66 year: 2019 ident: 365_CR24 publication-title: Pramana-J. Phys. – volume: 365 start-page: 345 issue: 5–6 year: 2007 ident: 365_CR29 publication-title: Phys. Lett. A doi: 10.1016/j.physleta.2007.01.046 – volume: 59 start-page: 3029 issue: 5 year: 2020 ident: 365_CR36 publication-title: Alex. Eng. J. doi: 10.1016/j.aej.2020.05.007 – volume: 260 start-page: 314 year: 2015 ident: 365_CR22 publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2015.03.037 – volume: 59 start-page: 2251 issue: 4 year: 2020 ident: 365_CR33 publication-title: Alex. Eng. J. doi: 10.1016/j.aej.2020.02.008 – volume: 5 start-page: 123 issue: 2 year: 2016 ident: 365_CR6 publication-title: Nonlinear Eng.-Model. Appl. – volume: 207 start-page: 285 issue: 2 year: 2004 ident: 365_CR38 publication-title: J. Differ. Equ. doi: 10.1016/j.jde.2004.07.026 – volume: 12 start-page: 1 issue: 17 year: 2020 ident: 365_CR9 publication-title: Symmetry. – volume: 139 start-page: 1 year: 2020 ident: 365_CR20 publication-title: Chaos Solitons Fract. doi: 10.1016/j.chaos.2020.110096 – volume: 1 start-page: 73 year: 2015 ident: 365_CR59 publication-title: Prog. Fract. Differ. Appl. – volume: 180 start-page: 708 year: 2009 ident: 365_CR47 publication-title: Comput. Phys. Commun. doi: 10.1016/j.cpc.2008.11.012 – volume: 346 start-page: 247 issue: 15 year: 2020 ident: 365_CR34 publication-title: J. Comput. Appl. Math. – volume: 2050149 start-page: 1 year: 2020 ident: 365_CR40 publication-title: Int. J. Mod. Phys. B doi: 10.1142/S0217979220501490 – volume: 59 start-page: 2149 issue: 4 year: 2020 ident: 365_CR10 publication-title: Alex. Eng. J. doi: 10.1016/j.aej.2020.01.032 – volume: 8 start-page: 164 year: 2019 ident: 365_CR17 publication-title: Nonlinear Eng.-Model. Appl. doi: 10.1515/nleng-2018-0001 |
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| SubjectTerms | Applications of Mathematics Field theory Mathematics Mathematics and Statistics Numerical analysis Operators (mathematics) Original Research Perturbation Quantum field theory Quantum theory |
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| Title | Numerical analysis of nonlinear fractional Klein–Fock–Gordon equation arising in quantum field theory via Caputo–Fabrizio fractional operator |
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