On Approximate Solution of Fractional Differential Equations with Variable Coefficients

In this paper we study some interesting properties of shifted Jacobi polynomials and based on these properties a new operational matrix is derived. The new matrix is then used along with some previous results to provide a theoretical treatment to approximate the solution of fractional differential equations with variable coefficients. The scheme is then extended to solve coupled system of fractional differential equations with variable coefficients. The scheme is simple and provides a very high accurate estimate of solution. The accuracy of the scheme is shown with some test problems. The results are displayed graphically. We use MatLab to carry out the necessary calculation.