Solution of Fractional Order Differential-Difference Equation by Using Laplace Transform Method.

Abstract

In this paper, we have proved  solution of a non-homogeneous fractional differential-difference equation of a general fractional order α and difference order 1 with general initial conditions with the help of Laplace Transform  where the fractional derivative  we are using  is in accordance with the definition of fractional derivative as  Caputo fractional derivative. A few examples are illustrated that support the results..The theorem  is proved on the solution of fractional order Differential difference equation. The existence and uniqueness of solution is given by existence of  laplace transform.