Using a numerical method by omitting discretization of data to study numerical solutions for boundary value problems of fractional order differential equations

Abstract

This manuscript is concerned to the numerical solutions by using shifted Jacobi polynomials (SJPs). By means of these polynomials, we construct some operational matrices (OMs) of fractional order integration and differentiation omitting collocations or discretization of data. With the help of these OMs, we establish a numerical method for the solutions of boundary value problems (BVPs) of fractional order differential equations (FODEs). The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations, which greatly simplifying the problems. These algebraic equations can be easily solved by using the computational software like Matlab and Mathematica. We provide some examples to demonstrate the procedure of our proposed method. Throughout the paper, we will use the Caputo fractional order derivative.