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

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.

کلیدواژه ها:

Fractional Volterra integro-differential equations ، cubic Hermite spline functions ، Caputo derivative ، Operational matrix