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A Convergent Collocation Approach for Generalized Fractional Integro-Differential Equations Using Jacobi Poly-Fractonomials

Author

Listed:
  • Sandeep Kumar

    (Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, Varanasi 221005, Uttar Pradesh, India)

  • Rajesh K. Pandey

    (Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, Varanasi 221005, Uttar Pradesh, India)

  • H. M. Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan
    Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy)

  • G. N. Singh

    (Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, Jharkhand, India)

Abstract

In this paper, we present a convergent collocation method with which to find the numerical solution of a generalized fractional integro-differential equation (GFIDE). The presented approach is based on the collocation method using Jacobi poly-fractonomials. The GFIDE is defined in terms of the B-operator introduced recently, and it reduces to Caputo fractional derivative and other fractional derivatives in special cases. The convergence and error analysis of the proposed method are also established. Linear and nonlinear cases of the considered GFIDEs are numerically solved and simulation results are presented to validate the theoretical results.

Suggested Citation

  • Sandeep Kumar & Rajesh K. Pandey & H. M. Srivastava & G. N. Singh, 2021. "A Convergent Collocation Approach for Generalized Fractional Integro-Differential Equations Using Jacobi Poly-Fractonomials," Mathematics, MDPI, vol. 9(9), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:979-:d:544505
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    Cited by:

    1. Hari M. Srivastava & Khaled Mohammed Saad & Walid M. Hamanah, 2022. "Certain New Models of the Multi-Space Fractal-Fractional Kuramoto-Sivashinsky and Korteweg-de Vries Equations," Mathematics, MDPI, vol. 10(7), pages 1-13, March.

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