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Computational algorithm for solving fredholm time-fractional partial integrodifferential equations of dirichlet functions type with error estimates

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  • Al-Smadi, Mohammed
  • Arqub, Omar Abu

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.

Suggested Citation

  • Al-Smadi, Mohammed & Arqub, Omar Abu, 2019. "Computational algorithm for solving fredholm time-fractional partial integrodifferential equations of dirichlet functions type with error estimates," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 280-294.
    • Handle: RePEc:eee:apmaco:v:342:y:2019:i:c:p:280-294
    DOI: 10.1016/j.amc.2018.09.020
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    1. El-Ajou, Ahmad & Abu Arqub, Omar & Momani, Shaher & Baleanu, Dumitru & Alsaedi, Ahmed, 2015. "A novel expansion iterative method for solving linear partial differential equations of fractional order," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 119-133.
    2. Devendra Kumar & Jagdev Singh & A. Kılıçman, 2013. "An Efficient Approach for Fractional Harry Dym Equation by Using Sumudu Transform," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, May.
    3. Singh, Jagdev & Kumar, Devendra & Hammouch, Zakia & Atangana, Abdon, 2018. "A fractional epidemiological model for computer viruses pertaining to a new fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 504-515.
    4. Emran Tohidi & M. M. Ezadkhah & S. Shateyi, 2014. "Numerical Solution of Nonlinear Fractional Volterra Integro-Differential Equations via Bernoulli Polynomials," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, March.
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    Cited by:

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    15. Abu Arqub, Omar & Maayah, Banan, 2019. "Modulation of reproducing kernel Hilbert space method for numerical solutions of Riccati and Bernoulli equations in the Atangana-Baleanu fractional sense," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 163-170.
    16. Saha Ray, S. & Singh, P., 2021. "Numerical solution of stochastic Itô-Volterra integral equation by using Shifted Jacobi operational matrix method," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    17. Hussam Aljarrah & Mohammad Alaroud & Anuar Ishak & Maslina Darus, 2021. "Adaptation of Residual-Error Series Algorithm to Handle Fractional System of Partial Differential Equations," Mathematics, MDPI, vol. 9(22), pages 1-17, November.
    18. Omar Abu Arqub & Mohamed S. Osman & Abdel-Haleem Abdel-Aty & Abdel-Baset A. Mohamed & Shaher Momani, 2020. "A Numerical Algorithm for the Solutions of ABC Singular Lane–Emden Type Models Arising in Astrophysics Using Reproducing Kernel Discretization Method," Mathematics, MDPI, vol. 8(6), pages 1-15, June.
    19. Hasan, Shatha & Al-Smadi, Mohammed & El-Ajou, Ahmad & Momani, Shaher & Hadid, Samir & Al-Zhour, Zeyad, 2021. "Numerical approach in the Hilbert space to solve a fuzzy Atangana-Baleanu fractional hybrid system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    20. Arqub, Omar Abu & Maayah, Banan, 2019. "Fitted fractional reproducing kernel algorithm for the numerical solutions of ABC – Fractional Volterra integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 394-402.
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