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

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.

Abstract

In this article, we solve systems of fractional Volterra integro-differential equations in the sense of the Caputo fractional derivative, using cubic Hermite spline functions. We first construct the operational matrix for the fractional derivative of the cubic Hermite spline functions. Then, using this matrix and key properties of these functions, we transform systems of fractional Volterra integro-differential equations into a system of algebraic equations, which can be solved numerically to obtain approximate solutions. Numerous examples show that the results obtained by this method align closely with the results presented by some previous works.

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Main Subjects

Computational Methods for Differential Equations
Volume 13, Issue 3
July 2025
Pages 980-994

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History

  • Receive Date: 12 July 2024
  • Revise Date: 10 April 2025
  • Accept Date: 19 April 2025

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