Fractional Order Alpha Laplace and Extorial Transform by Inverse difference Operator

摘要

In this article, the researchers tries to prove that alpha Laplace transform can be applied to fractional system. By defining, alpha difference operator, the researchers tries to prove, several properties of the inverse fractional difference operator, we define a fractional alpha Laplace transform, denoted by L~v_(a(h)) and fractional extorial transform, denoted by E~v_(a(h)) on time(t). Several identities, involving fractional difference operators are obtained for raising and falling h-factorials and Laplace and extorial transforms of factorial, geometric and logarithmic functions are also presented. Examples with diagrams, verified and generated by MATLAB, are provided as illustrations for the results presented.