Operational discrete Petrov-Galerkin method for solving distributed order FDEs

Articles in Press

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran.

10.22034/cmde.2026.71162.3579

Abstract

This study presents a novel discrete Petrov-Galerkin method for solving distributed-order fractional differential equations, where fractional derivatives are expressed in the Caputo sense. The proposed approach begins by reducing the distributed-order equation to a multi-term fractional equation using the Newton-Cotes quadrature rule, thereby simplifying the numerical approximation process. The discrete Petrov-Galerkin framework utilizes generalized Jacobi polynomials as basis functions and fractional Legendre functions as test functions, chosen for their robust approximation capabilities. By exploiting these mathematical properties, the method transforms the problem into a system of algebraic equations. A comprehensive convergence analysis is conducted to validate the accuracy and reliability of the method. The effectiveness of the proposed approach is further illustrated through three numerical examples, demonstrating its superior performance compared to existing techniques in terms of accuracy and computational efficiency.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 16 May 2026

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History

  • Receive Date: 10 January 2026
  • Revise Date: 12 May 2026
  • Accept Date: 13 May 2026

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