A New Computational Method Based on Fractional Integration Operational Matrices for Solving Fractional Integro–Differential Equations

Mehdi Delkhosh

International Journal of Differential Equations, 2026, vol. 2026, 1-13

Abstract: This paper presents a new numerical method for solving fractional integro–differential equations. After introducing the necessary preliminary definitions, fractional integration operational matrices are constructed based on fractional Lagrange functions, employed here as fractional basis functions. Operational matrices are employed to overcome the primary challenge of evaluating fractional integrals in the numerical solution of fractional differential and integral equations. These matrices are derived using the Riemann–Liouville fractional integral and subsequently used to formulate a novel numerical method. To validate the method, several theorems are stated concerning the accuracy, efficiency, and convergence, and the method is applied to solve some well-known benchmark differential equations.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:4658137

DOI: 10.1155/ijde/4658137

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