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Theoretical and computational analysis of nonlinear fractional integro-differential equations via collocation method

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  • Amin, Rohul
  • Ahmad, Hijaz
  • Shah, Kamal
  • Bilal Hafeez, M.
  • Sumelka, W.

Abstract

In this article, a class of nonlinear Volterra-Fredholm fractional integro-differential equations is considered, both theoretical and computational aspects. The respective theoretical results are devoted to the existence of a solution via fixed point approach. Further, for the computational aspect, the Proposed Methodology of Haar wavelet collocation. This method minimizes a system of nonlinear algebraic equations, which is developed by Broyden’s method. In literature, the proposed method is taken for checking the convergence with help of some numerical examples. Calculate mean square root and maximum absolute errors for various collocation point numbers. The final outcomes show that the applied Haar method is effective, and the convergence rate for different collocation point is roughly equal to 2.

Suggested Citation

  • Amin, Rohul & Ahmad, Hijaz & Shah, Kamal & Bilal Hafeez, M. & Sumelka, W., 2021. "Theoretical and computational analysis of nonlinear fractional integro-differential equations via collocation method," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    • Handle: RePEc:eee:chsofr:v:151:y:2021:i:c:s0960077921006068
    DOI: 10.1016/j.chaos.2021.111252
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    References listed on IDEAS

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    1. Raberto, Marco & Scalas, Enrico & Mainardi, Francesco, 2002. "Waiting-times and returns in high-frequency financial data: an empirical study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 749-755.
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    Cited by:

    1. Sondos M. Syam & Z. Siri & Sami H. Altoum & R. Md. Kasmani, 2023. "An Efficient Numerical Approach for Solving Systems of Fractional Problems and Their Applications in Science," Mathematics, MDPI, vol. 11(14), pages 1-21, July.

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