Cubic Hermit spline functions for the solution of fractional differential equations

Abstract

In this article, we solve fractional differential equations in the Caputo farctional 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 a fractional differential equation 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.