Numerical solution of fractional advection-diffusion equation with generalized Caputo derivative using shifted ultraspherical collocation method

Authors

  • K. Issa
    Department of Mathematics and Statistics, Kwara State University, Malete, Nigeria
  • A. T. AbdulKareem
    Department of Mathematics and Statistics, Kwara State University, Malete, Nigeria
  • A D. Adeshola
    Department of Mathematics and Statistics, Kwara State University, Malete, Nigeria
  • R. A. Bello
    Department of Mathematics and Statistics, Kwara State University, Malete, Nigeria

Keywords:

Ultraspherical collocation method, Generalized Caputo Fractional Derivative (GCFD), Shifted ultraspherical polynomial, Fractional advection-diffusion equation, Finite difference scheme

Abstract

In this article, we develop an approximate technique for solving a fractional advection-diffusion equation with a generalized Caputo derivative via a finite difference scheme. This technique employed the properties of shifted ultraspherical polynomials, which combine the finite difference scheme for the temporal discretization derivative and express the approximate solution in terms of shifted ultraspherical polynomials. The convergence and the stability of the proposed technique are proved. Numerical examples are considered, and the obtained results are compared with the analytical results and those obtained in the literature to establish the accuracy of the technique. The proposed techniques, based on the generalized Caputo derivative and the properties of shifted ultraspherical polynomials, produce robust results and encompass those obtained using several other families of orthogonal polynomials as demonstrated in the results of the examples considered.

Dimensions

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Published

2026-05-02

How to Cite

Numerical solution of fractional advection-diffusion equation with generalized Caputo derivative using shifted ultraspherical collocation method. (2026). Journal of the Nigerian Society of Physical Sciences, 8(2), 2986. https://doi.org/10.46481/jnsps.2026.2986

Issue

Volume 8, Issue 2, May 2026 (In Progress)

Section

Mathematics & Statistics
Copyright & Licensing

Copyright (c) 2026 K. Issa, A. T. AbdulKareem, A D. Adeshola, R. A. Bello (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Numerical solution of fractional advection-diffusion equation with generalized Caputo derivative using shifted ultraspherical collocation method. (2026). Journal of the Nigerian Society of Physical Sciences, 8(2), 2986. https://doi.org/10.46481/jnsps.2026.2986

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