Shifted Fractional-Order Jacobi Collocation Method for Solving Variable-Order Fractional Integro-Differential Equation with Weakly Singular Kernel
We propose a fractional-order shifted Jacobi–Gauss collocation method for variable-order fractional integro-differential equations with weakly singular kernel (VO-FIDE-WSK) subject to initial conditions. Using the Riemann–Liouville fractional integral and derivative and fractional-order shifted Jaco...
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| Published in | Fractal and fractional Vol. 6; no. 1; p. 19 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
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Basel
MDPI AG
01.01.2022
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| Online Access | Get full text |
| ISSN | 2504-3110 2504-3110 |
| DOI | 10.3390/fractalfract6010019 |
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| Abstract | We propose a fractional-order shifted Jacobi–Gauss collocation method for variable-order fractional integro-differential equations with weakly singular kernel (VO-FIDE-WSK) subject to initial conditions. Using the Riemann–Liouville fractional integral and derivative and fractional-order shifted Jacobi polynomials, the approximate solutions of VO-FIDE-WSK are derived by solving systems of algebraic equations. The superior accuracy of the method is illustrated through several numerical examples. |
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| AbstractList | We propose a fractional-order shifted Jacobi–Gauss collocation method for variable-order fractional integro-differential equations with weakly singular kernel (VO-FIDE-WSK) subject to initial conditions. Using the Riemann–Liouville fractional integral and derivative and fractional-order shifted Jacobi polynomials, the approximate solutions of VO-FIDE-WSK are derived by solving systems of algebraic equations. The superior accuracy of the method is illustrated through several numerical examples. |
| Author | Babatin, Mohammed M. Abdelkawy, Mohamed A. Amin, Ahmed Z. M. Lopes, António M. Hashim, Ishak |
| Author_xml | – sequence: 1 givenname: Mohamed A. orcidid: 0000-0002-9043-9644 surname: Abdelkawy fullname: Abdelkawy, Mohamed A. – sequence: 2 givenname: Ahmed Z. M. orcidid: 0000-0003-4044-3335 surname: Amin fullname: Amin, Ahmed Z. M. – sequence: 3 givenname: António M. orcidid: 0000-0001-7359-4370 surname: Lopes fullname: Lopes, António M. – sequence: 4 givenname: Ishak orcidid: 0000-0003-4237-7140 surname: Hashim fullname: Hashim, Ishak – sequence: 5 givenname: Mohammed M. surname: Babatin fullname: Babatin, Mohammed M. |
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| Cites_doi | 10.1515/ijnsns-2016-0160 10.1007/s11075-013-9710-2 10.1016/j.cnsns.2015.10.027 10.1177/1077546315581228 10.1016/j.jcp.2015.03.063 10.1016/j.camwa.2013.01.023 10.1016/j.jcp.2012.03.001 10.1063/1.4958717 10.1016/j.camwa.2010.10.027 10.1016/j.cam.2013.07.044 10.1007/s11071-014-1854-7 10.1016/j.camwa.2013.10.011 10.1155/2016/6345978 10.1016/j.cam.2016.06.012 10.1080/00207160.2014.964692 10.1016/j.apnum.2017.06.010 10.1016/j.cnsns.2019.01.005 10.1016/j.cnsns.2011.04.025 10.1016/j.aml.2015.02.010 10.1155/2015/902161 10.1016/j.cam.2011.06.019 10.1007/s11075-011-9465-6 10.1007/978-3-540-30728-0 10.1016/j.apnum.2016.07.011 10.1007/s11071-018-4366-z 10.1016/j.apnum.2013.11.003 10.1016/j.mcm.2011.01.002 10.2298/TSCI180320239Y 10.3233/FI-2017-1479 10.1016/j.jcp.2014.03.039 10.1140/epjst/e2018-00020-2 10.1016/j.camwa.2016.11.019 10.1016/j.mcm.2011.09.034 10.1142/9789814355216 10.1155/2013/586870 10.1016/j.jcp.2014.12.043 10.1016/j.camwa.2011.12.050 10.1016/j.jcp.2013.09.039 10.1137/S0036142902410271 10.1016/j.jcp.2014.08.015 10.1007/s40314-020-1070-7 10.1016/j.jcp.2014.12.001 10.3846/13926292.2017.1258014 10.1016/j.apm.2015.10.009 10.1016/j.chaos.2020.109721 10.1016/j.apacoust.2013.12.010 |
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| References | Nemati (ref_12) 2016; 308 Zayernouri (ref_29) 2015; 293 Doha (ref_47) 2012; 64 Alikhanov (ref_33) 2015; 268 ref_53 Lin (ref_38) 2009; 212 Yi (ref_16) 2016; 40 Shen (ref_49) 2003; 41 Abdelkawy (ref_57) 2020; 134 Doha (ref_43) 2014; 77 Chen (ref_22) 2015; 46 Yang (ref_8) 2019; 23 Chen (ref_32) 2014; 68 Yang (ref_51) 2013; 225 Abdelkawy (ref_58) 2020; 39 Wang (ref_13) 2016; 275 Okuzono (ref_54) 2014; 79 Atangana (ref_27) 2015; 293 Liu (ref_36) 2016; 2016 Eslahchi (ref_2) 2014; 257 Abdelkawy (ref_1) 2015; 1 Momani (ref_11) 2006; 182 Chen (ref_24) 2014; 238 Ghoreishi (ref_44) 2011; 61 Abdelkawy (ref_42) 2017; 18 Yang (ref_6) 2017; 226 Sun (ref_23) 2015; 2015 Mokhtary (ref_45) 2011; 58 Bhrawy (ref_46) 2015; 293 Xu (ref_21) 2014; 40 Pedas (ref_17) 2016; 110 Chen (ref_37) 2011; 236 Chen (ref_48) 2012; 231 Mokhtary (ref_15) 2017; 121 Bhrawy (ref_41) 2013; 222 Yi (ref_19) 2015; 92 Bhrawy (ref_55) 2017; 73 Yang (ref_7) 2017; 151 Wen (ref_52) 2014; 67 Bhrawy (ref_40) 2016; 4 Tavares (ref_26) 2016; 35 Zaky (ref_56) 2018; 94 Bhrawy (ref_4) 2015; 294 Zhang (ref_28) 2014; 242 Zayernouri (ref_5) 2014; 257 Doha (ref_20) 2019; 72 Bhrawy (ref_25) 2015; 80 Zhao (ref_14) 2014; 65 Bhrawy (ref_39) 2012; 17 Razminia (ref_35) 2012; 55 Doha (ref_50) 2011; 53 ref_3 Alqahtani (ref_30) 2017; 22 Lopes (ref_10) 2016; 22 Zhao (ref_31) 2015; 293 Chen (ref_9) 2016; 26 Sweilam (ref_34) 2013; 2013 Bhrawy (ref_18) 2018; 47 |
| References_xml | – volume: 238 start-page: 329 year: 2014 ident: ref_24 article-title: Numerical solution for the variable order linear cable equation with Bernstein polynomials publication-title: Appl. Math. Comput. – volume: 18 start-page: 411 year: 2017 ident: ref_42 article-title: Jacobi collocation approximation for solving multi-dimensional Volterra integral equations publication-title: Int. J. Nonlinear Sci. Numer. Simul. doi: 10.1515/ijnsns-2016-0160 – volume: 65 start-page: 723 year: 2014 ident: ref_14 article-title: Collocation methods for fractional integro-differential equations with weakly singular kernels publication-title: Numer. Algorithms doi: 10.1007/s11075-013-9710-2 – volume: 35 start-page: 69 year: 2016 ident: ref_26 article-title: Caputo derivatives of fractional variable order: Numerical approximations publication-title: Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2015.10.027 – volume: 22 start-page: 2100 year: 2016 ident: ref_10 article-title: Modeling vegetable fractals by means of fractional-order equations publication-title: J. Vib. Control doi: 10.1177/1077546315581228 – volume: 294 start-page: 462 year: 2015 ident: ref_4 article-title: A fully spectral collocation approximation for multi-dimensional fractional Schrödinger equations publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2015.03.063 – volume: 68 start-page: 2133 year: 2014 ident: ref_32 article-title: Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2013.01.023 – volume: 231 start-page: 5016 year: 2012 ident: ref_48 article-title: Efficient spectral-Galerkin methods for systems of coupled second-order equations and their applications publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2012.03.001 – volume: 26 start-page: 084303 year: 2016 ident: ref_9 article-title: Design and implementation of grid multi-scroll fractional-order chaotic attractors publication-title: Chaos Interdiscip. J. Nonlinear Sci. doi: 10.1063/1.4958717 – volume: 61 start-page: 30 year: 2011 ident: ref_44 article-title: An extension of the spectral Tau method for numerical solution of multi-order fractional differential equations with convergence analysis publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2010.10.027 – volume: 257 start-page: 105 year: 2014 ident: ref_2 article-title: Application of the collocation method for solving nonlinear fractional integro-differential equations publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2013.07.044 – volume: 80 start-page: 101 year: 2015 ident: ref_25 article-title: Numerical simulation for two-dimensional variable-order fractional nonlinear cable equation publication-title: Nonlinear Dyn. doi: 10.1007/s11071-014-1854-7 – volume: 67 start-page: 1 year: 2014 ident: ref_52 article-title: Convergence analysis of a new multiscale finite element method for the stationary Navier–Stokes problem publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2013.10.011 – volume: 2016 start-page: 6345978 year: 2016 ident: ref_36 article-title: An operational matrix technique for solving variable order fractional differential-integral equation based on the second kind of Chebyshev polynomials publication-title: Adv. Math. Phys. doi: 10.1155/2016/6345978 – volume: 308 start-page: 231 year: 2016 ident: ref_12 article-title: A fast numerical algorithm based on the second kind Chebyshev polynomials for fractional integro-differential equations with weakly singular kernels publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2016.06.012 – volume: 225 start-page: 407 year: 2013 ident: ref_51 article-title: An approximation of semiconductor device by mixed finite element method and characteristics-mixed finite element method publication-title: Appl. Math. Comput. – volume: 92 start-page: 1715 year: 2015 ident: ref_19 article-title: CAS wavelet method for solving the fractional integro-differential equation with a weakly singular kernel publication-title: Int. J. Comput. Math. doi: 10.1080/00207160.2014.964692 – volume: 121 start-page: 52 year: 2017 ident: ref_15 article-title: Numerical analysis of an operational Jacobi Tau method for fractional weakly singular integro-differential equations publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2017.06.010 – volume: 72 start-page: 342 year: 2019 ident: ref_20 article-title: Shifted Jacobi–Gauss-collocation with convergence analysis for fractional integro-differential equations publication-title: Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2019.01.005 – volume: 40 start-page: 699 year: 2014 ident: ref_21 article-title: A finite difference technique for solving variable-order fractional integro-differential equations publication-title: Bull. Iran. Math. Soc. – volume: 17 start-page: 62 year: 2012 ident: ref_39 article-title: A Jacobi–Gauss collocation method for solving nonlinear Lane–Emden type equations publication-title: Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2011.04.025 – volume: 46 start-page: 83 year: 2015 ident: ref_22 article-title: Numerical solution for a class of nonlinear variable order fractional differential equations with Legendre wavelets publication-title: Appl. Math. Lett. doi: 10.1016/j.aml.2015.02.010 – volume: 2015 start-page: 902161 year: 2015 ident: ref_23 article-title: Numerical algorithm to solve a class of variable order fractional integral-differential equation based on Chebyshev polynomials publication-title: Math. Probl. Eng. doi: 10.1155/2015/902161 – volume: 236 start-page: 209 year: 2011 ident: ref_37 article-title: Numerical analysis for a variable-order nonlinear cable equation publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2011.06.019 – volume: 58 start-page: 475 year: 2011 ident: ref_45 article-title: The L2-convergence of the Legendre spectral Tau matrix formulation for nonlinear fractional integro differential equations publication-title: Numer. Algorithms doi: 10.1007/s11075-011-9465-6 – ident: ref_53 doi: 10.1007/978-3-540-30728-0 – volume: 110 start-page: 204 year: 2016 ident: ref_17 article-title: Spline collocation for fractional weakly singular integro-differential equations publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2016.07.011 – volume: 94 start-page: 757 year: 2018 ident: ref_56 article-title: Correction to: Numerical simulation for two-dimensional variable-order fractional nonlinear cable equation publication-title: Nonlinear Dyn. doi: 10.1007/s11071-018-4366-z – volume: 77 start-page: 43 year: 2014 ident: ref_43 article-title: A new Jacobi rational–Gauss collocation method for numerical solution of generalized pantograph equations publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2013.11.003 – volume: 222 start-page: 255 year: 2013 ident: ref_41 article-title: A Jacobi–Gauss–Lobatto collocation method for solving generalized Fitzhugh–Nagumo equation with time-dependent coefficients publication-title: Appl. Math. Comput. – volume: 53 start-page: 1820 year: 2011 ident: ref_50 article-title: A Jacobi–Jacobi dual-Petrov–Galerkin method for third-and fifth-order differential equations publication-title: Math. Comput. Model. doi: 10.1016/j.mcm.2011.01.002 – volume: 23 start-page: 1677 year: 2019 ident: ref_8 article-title: A new general fractional-order derivataive with Rabotnov fractional-exponential kernel applied to model the anomalous heat transfer publication-title: Therm. Sci. doi: 10.2298/TSCI180320239Y – volume: 47 start-page: 553 year: 2018 ident: ref_18 article-title: A spectral technique for solving two-dimensional fractional integral equations with weakly singular kernel publication-title: Hacet. J. Math. Stat. – volume: 151 start-page: 63 year: 2017 ident: ref_7 article-title: A new family of the local fractional PDEs publication-title: Fundam. Informaticae doi: 10.3233/FI-2017-1479 – volume: 293 start-page: 142 year: 2015 ident: ref_46 article-title: A spectral tau algorithm based on Jacobi operational matrix for numerical solution of time fractional diffusion-wave equations publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2014.03.039 – volume: 268 start-page: 12 year: 2015 ident: ref_33 article-title: Numerical methods of solutions of boundary value problems for the multi-term variable-distributed order diffusion equation publication-title: Appl. Math. Comput. – volume: 226 start-page: 3567 year: 2017 ident: ref_6 article-title: A new fractional derivative involving the normalized sinc function without singular kernel publication-title: Eur. Phys. J. Spec. Top. doi: 10.1140/epjst/e2018-00020-2 – volume: 182 start-page: 754 year: 2006 ident: ref_11 article-title: Numerical methods for fourth-order fractional integro-differential equations publication-title: Appl. Math. Comput. – volume: 1 start-page: 1 year: 2015 ident: ref_1 article-title: A Jacobi spectral collocation scheme for solving Abel’s integral equations publication-title: Prog. Fract. Differ. Appl. – volume: 73 start-page: 1100 year: 2017 ident: ref_55 article-title: Highly accurate numerical schemes for multi-dimensional space variable-order fractional Schrödinger equations publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2016.11.019 – volume: 4 start-page: 1 year: 2016 ident: ref_40 article-title: Legendre–Gauss–Lobatto collocation method for solving multi-dimensional Fredholm integral equations publication-title: Comput. Math. Appl. – volume: 55 start-page: 1106 year: 2012 ident: ref_35 article-title: Solution existence for non-autonomous variable-order fractional differential equations publication-title: Math. Comput. Model. doi: 10.1016/j.mcm.2011.09.034 – ident: ref_3 doi: 10.1142/9789814355216 – volume: 2013 start-page: 586870 year: 2013 ident: ref_34 article-title: Numerical simulations for the space-time variable order nonlinear fractional wave equation publication-title: J. Appl. Math. doi: 10.1155/2013/586870 – volume: 293 start-page: 104 year: 2015 ident: ref_27 article-title: On the stability and convergence of the time-fractional variable order telegraph equation publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2014.12.043 – volume: 242 start-page: 541 year: 2014 ident: ref_28 article-title: Numerical analysis of a new space–time variable fractional order advection–dispersion equation publication-title: Appl. Math. Comput. – volume: 64 start-page: 558 year: 2012 ident: ref_47 article-title: An efficient direct solver for multidimensional elliptic Robin boundary value problems using a Legendre spectral-Galerkin method publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2011.12.050 – volume: 257 start-page: 460 year: 2014 ident: ref_5 article-title: Exponentially accurate spectral and spectral element methods for fractional ODEs publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2013.09.039 – volume: 41 start-page: 1595 year: 2003 ident: ref_49 article-title: A new dual-Petrov-Galerkin method for third and higher odd-order differential equations: Application to the KDV equation publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142902410271 – volume: 275 start-page: 72 year: 2016 ident: ref_13 article-title: SCW method for solving the fractional integro-differential equations with a weakly singular kernel publication-title: Appl. Math. Comput. – volume: 293 start-page: 184 year: 2015 ident: ref_31 article-title: Second-order approximations for variable order fractional derivatives: Algorithms and applications publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2014.08.015 – volume: 39 start-page: 1 year: 2020 ident: ref_58 article-title: Highly accurate technique for solving distributed-order time-fractional-sub-diffusion equations of fourth order publication-title: Comput. Appl. Math. doi: 10.1007/s40314-020-1070-7 – volume: 293 start-page: 312 year: 2015 ident: ref_29 article-title: Fractional spectral collocation methods for linear and nonlinear variable order FPDEs publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2014.12.001 – volume: 22 start-page: 1 year: 2017 ident: ref_30 article-title: Space-time spectral collocation algorithm for the variable-order Galilei invariant advection diffusion equations with a nonlinear source term publication-title: Math. Model. Anal. doi: 10.3846/13926292.2017.1258014 – volume: 40 start-page: 3422 year: 2016 ident: ref_16 article-title: Legendre wavelets method for the numerical solution of fractional integro-differential equations with weakly singular kernel publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2015.10.009 – volume: 212 start-page: 435 year: 2009 ident: ref_38 article-title: Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation publication-title: Appl. Math. Comput. – volume: 134 start-page: 109721 year: 2020 ident: ref_57 article-title: Shifted fractional Jacobi collocation method for solving fractional functional differential equations of variable order publication-title: Chaos Solitons Fractals doi: 10.1016/j.chaos.2020.109721 – volume: 79 start-page: 1 year: 2014 ident: ref_54 article-title: A finite-element method using dispersion reduced spline elements for room acoustics simulation publication-title: Appl. Acoust. doi: 10.1016/j.apacoust.2013.12.010 |
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| SubjectTerms | Algorithms Approximation Boundary conditions Collocation methods Derivatives Differential equations Fractional calculus fractional-order shifted Jacobi polynomial Initial conditions Integrals Kernels Polynomials Riemann–Liouville fractional derivative Riemann–Liouville fractional integral variable-order fractional integro-differential equation |
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| Title | Shifted Fractional-Order Jacobi Collocation Method for Solving Variable-Order Fractional Integro-Differential Equation with Weakly Singular Kernel |
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