An approximate approach for fractional singular delay integro-differential equations

Abstract

In this article, we present Jacobi-Gauss collocation method to numerically solve the fractional singular delay integro-differential equations, because such methods have better superiority, capability and applicability than other methods. We first apply a technique to replace the delay function in the considered equation and suggest an equivalent system. We then propose a Jacobi-Gauss collocation approach to discretize the obtained system and to achieve an algebraic system. Having solved the algebraic system, an approximate solution is gained for the original equation. Three numerical examples are solved to show the applicability of presented approximate approach. Obtaining the approximations of the solution and its fractional derivative simultaneously and an acceptable approximation by selecting a small number of collocation points are advantages of the suggested method.

Keywords

• caputo and riemann-liouville fractional derivatives
• fractional singular delay integro-differential equations
• jacobi-gauss points
• lagrange interpolation polynomial