Laplace transform method for linear sequential Riemann Liouville and Caputo fractional differential equations

Abstract

Study of nonlinear sequential fractional differential equations of Riemann-Lioville type and Caputo type initial value problem are very useful in applications. In order to develop any iterative methods to solve the nonlinear problems, we need to solve the corresponding linear problem. In this work, we develop Laplace transform method to solve the linear sequential Riemann-Liouville fractional differential equations as well as linear sequential Caputo fractional differential equations of order nq which is sequential of order q. Also, nq is chosen such that (n−1) < nq < n. All our results yield the integer results as a special case when q tends to 1.