Some analytical results on the ∆−fractional dynamic equations

Abstract

In this paper, we successfully solve some linear ∆−fractional dynamic equations (∆−FDE) with Caputo ∆−derivative analytically by solving an auxiliary linear ∆−differential equation (∆−DE) with an integer order. The idea of the proposed method is based on transforming the given ∆−FDE into a linear ∆−DE with an integer order. This transformation removes certain terms of the solution of the considered ∆−FDE, resulting in the remaining terms being a solution to the auxiliary equation. To demonstrate the ability and efficacy of this idea, several examples have been provided.