Laplace transform method for sequential Caputo fractional differential equations

Abstract

Solutions of linear sequential Caputo fractional differential equation with constant coefficients and with initial conditions of order nq; can be obtained using the Laplace transform method. Here n-􀀀1<nq<n: If q=1; the results of integer results of order n can be obtained as a special case. We obtain solutions of linear sequential Caputo fractional differential equations of order nq in terms of Mittag-Leffler functions and/or combination of them, of order q only. In this work, we present the results of order 2q only, which can easily be extended to any nq: As an application of this approach, we obtain the representation form for the solution of the initial value problem of the fractional order 2q: We can also obtain a representation form for fractional sub hyperbolic equation of order 2q in
time, in one dimensional space. All our results yield the integer order results as a special case.