A new fractional collocation method for a system of multi-order fractional differential equations with variable coefficients

Abstract

This paper is concerned with a new fractional Jacobi collocation method for solving a system of multi-order fractional differential equations with variable coefficients. The existence, uniqueness, and smoothness results are rigorously studied. From the numerical point of view, first a new interpolation operator based on the orthogonal fractional Jacobi functions as well as its approximation properties are provided, and then it is employed to obtain collocation solution of the underlying problem. Moreover, the convergence analysis of the proposed scheme is investigated in both L∞ and L2 norms. Finally, the applicability and validity of the method are demonstrated by means of some illustrative examples.