Fractional pseudospectral integration/differentiation matrix and fractional differential equations

摘要

In this paper, we present a new pseudospectral integration matrix which can be used to compute n−fold integrals of function f for any n∈R+. Also, it can be used to calculate the derivatives of f for any non-integer order α  <  0. We use the Chebyshev interpolating polynomial for f at the Gauss–Lobatto points in [−1,1]. Less computational complexity and programming, much higher rate in running, calculating the integral/derivative of fractional order and its extraordinary accuracy, are advantages of this method in comparison with other known methods. We apply two approaches by using this matrix to solve some fractional differential equations with high accuracy. Some numerical examples are presented.