Novel Legendre-Jaiswal functions for solving time-space fractional partial differential equations

Articles in Press

Document Type : Research Article

Authors

1 Department of Mathematics National Institute of Technology Rourkela

2 Department of Mathematics, NIT Rourkela, Odisha, India

Abstract

This paper examines a new fractional function based on Legendre and Jaiswal polynomials to solve linear and nonlinear time-space fractional partial differential equations of linear and nonlinear class. The Caputo sense is applied while using the fractional derivative. These problems can be solved using the collocation method, operational, and pseudo-operational matrices of integer and fractional-order integration. Using operational matrices, pseudo-operational matrices, and the collocation method, the problem is transformed into a system of algebraic equations. An upper bound on the error of the fractional-order integral operational matrix is computed. Furthermore, a detailed stability and convergence analysis of the collocation scheme presented to validate the robustness of the numerical approach. The applicability and effectiveness of the approach are demonstrated through several benchmark examples, including linear and non-linear fractional convection-diffusion, convection-diffusion-reaction, and nonlinear Fisher's equation. The numerical results confirm that the proposed method is stable, rapidly convergent, and highly accurate, outperforming several existing techniques in both efficiency and precision.

Keywords

Main Subjects

Journal of Mathematical Modeling

Articles in Press, Corrected Proof
Available Online from 21 December 2025

Files

Share

How to cite

Statistics