Efficient Computational Techniques for Fractional Order Delay-Integro Differential Equations

In this paper, we present Legendre - collocation method, together with the Gauss–Legendre quadrature integration for solving fractional order delay-integro differential equations (FDIDE) with Caputo fractional derivative. The properties of shifted Legendre polynomials are used to solve the FDIDE to system of equations. The equation system obtained is solved by using Newton iteration method based on our present method with numerical examples is shown both applicability and efficiency of method. The results obtained by the collocation method are compared with exact solution and is shown to be compatible. The Maple and MATLAB programs are used for the calculations required in the study.