- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 5 Issue: 2
- Shehu Transform of Hilfer-Prabhakar Fractional Derivatives and Applications on some Cauchy Type Prob...
Shehu Transform of Hilfer-Prabhakar Fractional Derivatives and Applications on some Cauchy Type Problems
Authors : Rachid BELGACEM, Ahmed BOKHARİ, Boualem SADAOUİ
Pages : 203-214
Doi:10.31197/atnaa.828468
View : 4 | Download : 2
Publication Date : 2021-06-30
Article Type : Research
Abstract :In this paper, we are interested on the Shehu transform of both Prabhakar and Hilfer–Prabhakar fractional derivative and its regularized version. These results are presented in terms of Mittag-Leffler type function and also utilized to obtain the solutions of some Cauchy type problems, such as Space-time Fractional Advection-Dispersion equation and Generalized fractional Free Electron Laser (FEL) equation, at which Hilfer-Prabhakar fractional derivative of fractional order and its regularized version are involved.Keywords : Hilfer–Prabhakar derivatives, Prabhakar integrals, Mittag–Leffler functions, Shehu transform