Solving system of fractional Volterra integro-differential equations using cubic Hermite spline functions

Lakestani, Mehrdad; Ghasemkhani, Roya; Allahviranloo, Tofigh

doi:10.22034/cmde.2025.62477.2756

Solving system of fractional Volterra integro-differential equations using cubic Hermite spline functions

Articles in Press

Document Type : Research Paper

Authors

¹ Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, Iran.

² Department of Mathematics, Faculty of Science, University of Jiroft, Jiroft, Iran.

³ Research Center of Performance and Productivity Analysis, Istinye University, Istanbul, Türkiye.

10.22034/cmde.2025.62477.2756

Abstract

In this article, we solve systems of fractional Volterra integro-differential equations in the Caputo fractional derivative sense using cubic Hermite spline functions. We first construct the operational matrix to the fractional derivative of the cubic Hermite spline functions. Then using this matrix and some properties of these functions, we convert systems of fractional Volterra integro-differential equations into a system of algebraic equations that can be solved to find the approximate solution. Numerous examples show that the results obtained by this method are in full agreement with the results presented by some previous works.

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