Govinda Pageni and Aghalaya S Vatsala. Study of Two System of Caputo Fractional Differential Equations with Initial Conditions via Laplace Transform Method.
Neural Parallel and Scientific Computations 29 (2021), No. 2,  69-83

https://doi.org/10.46719/npsc20212921

ABSTRACT.
In this work, we will provide an analytical method to compute the solution of the linear coupled system of Caputo fractional differential equations with initial conditions. The standard method adopted for the system of ordinary differential equations using the exponential of a matrix will not be useful, since the Mittag-Leffler function does not have the nice property of the exponential function. In addition, the variation of parameter cannot be adopted for fractional differential equations. Here we have used the Laplace transform method to solve the system of Caputo fractional differential equations when the order of the derivative is q and 0 < q < 1. The method yields the integer results as a special case. Our method also works for scalar sequential Caputo fractional differential equations of order nq, since it can be reduced to n systems of q-th order Caputo fractional differential equations with initial conditions.

AMS (MOS) Subject Classification. 34A12, 34A08.
Key Words: Mittag-Leffler Function, Caputo Fractional Derivative, Sequential.