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Numerical solutions for fractional initial value problems of distributed-order

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  • M. A. Abdelkawy

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia2Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt)

Abstract

This paper addresses spectral collocation techniques to treat with the fractional initial value problem of distributed-order. We introduce three algorithms based on shifted fractional order Jacobi orthogonal functions outputted by Jacobi polynomials. The shifted fractional order Jacobi–Gauss–Radau collocation method is developed for approximating the fractional initial value problem of distributed-order. The principal target in our techniques is to transform the fractional initial value problem of distributed-order to a system of algebraic equations. Some numerical examples are given to test the accuracy and applicability of our technique. It is known that the accuracy of numerical approaches for nonsmooth solution is deteriorated. Employing fractional order Jacobi functions instead of the classical Jacobi stopped this deterioration.

Suggested Citation

  • M. A. Abdelkawy, 2021. "Numerical solutions for fractional initial value problems of distributed-order," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 32(07), pages 1-13, July.
    • Handle: RePEc:wsi:ijmpcx:v:32:y:2021:i:07:n:s0129183121500960
    DOI: 10.1142/S0129183121500960
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    Cited by:

    1. Mohammed M. Al-Shomrani & Mohamed A. Abdelkawy & António M. Lopes, 2023. "Spectral Collocation Technique for Solving Two-Dimensional Multi-Term Time Fractional Viscoelastic Non-Newtonian Fluid Model," Mathematics, MDPI, vol. 11(9), pages 1-14, April.
    2. Faïçal Ndaïrou & Delfim F. M. Torres, 2021. "Pontryagin Maximum Principle for Distributed-Order Fractional Systems," Mathematics, MDPI, vol. 9(16), pages 1-12, August.

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