10.1007/s40096-022-00497-7

A Legendre-spectral method for Hadamard fractional partial differential equations

  • Ghafirlia Istafa1,
  • Mujeeb ur Rehman*1,
  1. School of Natural Sciences, National University of Sciences and Technology, H-12 Islamabad, PK

Published in Issue 2022-11-20

How to Cite

Istafa, G., & ur Rehman, M. (2022). A Legendre-spectral method for Hadamard fractional partial differential equations. Mathematical Sciences, 18(2 (June 2024). https://doi.org/10.1007/s40096-022-00497-7
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Abstract

Abstract In this paper, we present a spectral method to obtain numerical solutions of Caputo–Hadamard fractional partial differential equations. For better approximations, a modification of classical Legendre polynomials which is suitable for the Hadamard fractional operators is preferred. We utilized two-dimensional Hadamard fractional Legendre functions which are variants of two-dimensional shifted Legendre polynomials. Three different schemes for three classes of Caputo–Hadamard fractional partial differential equations are proposed and every scheme is accompanied by a numerical example to verify the applicability and efficiency of the suggested methods. Moreover, the estimates of upper bounds of error for the approximations have been derived.

Keywords

  • Fractional partial differential equations,
  • Two-dimensional Legendre functions,
  • Hadamard fractional Legendre functions

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