ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

The Generalized Laplace Transform and Fractional Dierential Equations of Distributed Orders


Alireza Ansari

Faculty of Mathematical Sciences
Shahrekord University,
P.O.Box 115, Shahrekord,


In this article, we introduce a new generalized Laplace transform and derive the complex inversion formula , convolution theorem and generalized product theorem for the transform. Furthermore, the fundamental solutions of two Cauchy type fractional diffusion equation of single and distributed order are given by means of new transform in terms of the Wright functions. Also, applicability of this transform in evaluation of improper integrals of special functions is stated.

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