Basic results for sequential Caputo fractional differential equations

Abstract

We have developed a representation form for the linear fractional differential equation of order q when 0 < q < 1, with variable coefficients. We have also obtained a closed form of the solution for sequential Caputo fractional differential equation of order 2q, with initial and boundary conditions, for 0 < 2q < 1: The solutions are in terms of Mittag-Leffler functions of order q only. Our results yield the known results of integer order when q = 1: We have also presented some numerical results to bring the salient features of sequential fractional differential equations.