Generalized Shehu Transform to $\Psi$-Hilfer-Prabhakar Fractional Derivative and its Regularized Version

Authors : Sachın MAGAR, Ahmed HAMOUD, Amol KHANDAGALE, Kirtiwant GHADLE

Pages : 364-379

View : 11 | Download : 6

Publication Date : 2022-09-30

Article Type : Research Paper

Abstract :In this manuscript, athours interested on the generalized Shehu transform of $\Psi$-Riemann-Liouville, $\Psi$-Caputo, $\Psi$-Hilfer fractional derivatives. Moreover, $\Psi$-Prabhakar, $\Psi$-Hilfer-Prabhakar fractional derivatives and its regularized version presented in terms of the $\Psi$-Mittag-Leffler type function. They are also utilised to solve several Cauchy type problems involving $\Psi$-Hilfer-Prabhakar fractional derivatives and their regularised form, such as the space-time fractional advection-dispersion equation and the generalized fractional free-electron laser insert ignore into journalissuearticles values(FEL); equation.
Keywords : Psi Prabhakar integral, Psi Hilfer Prabhakar derivative, Psi Mittag Leffler function, Psi Shehu transform