SOME ANALYTICAL RESULTS ON THE ∆−FRACTIONAL DYNAMIC EQUATIONS

SOME ANALYTICAL RESULTS ON THE ∆−FRACTIONAL DYNAMIC EQUATIONS

N. K. Mahdi, A. R. Khudair

[PDF]

Abstract

In this paper, we successfully solve some linear Δ−fractional dynamic equations (Δ−FDE) with Caputo Δ−derivative analytically by solving an auxiliary linear Δ−differential equation (Δ−DE) with an integer order. The idea of the proposed method is based on transforming the given Δ−FDE into a linear Δ−DE with an integer order. This transformation removes certain terms of the solution of the considered Δ−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.

Keywords

Time Scale Calculus, Fractional time scale calculus, Caputo fractional Δ− derivatives.