Sachin K. Magara, Ahmed A. Hamoudb, Amol D. Khandagaleb, Kirtiwant P. Ghadleb
a Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad-431004 (M.S.), India.
b Department of Mathematics, Taiz University, Taiz, Yemen.
In this manuscript, athours interested on the generalized Shehu transform of Ψ-Riemann-Liouville, Ψ-Caputo, Ψ-Hilfer fractional derivatives. Moreover, Ψ-Prabhakar, Ψ-Hilfer-Prabhakar fractional derivatives and its regularized version presented in terms of the Ψ-Mittag-Leffler type function.
They are also utilised to solve several Cauchy type problems involving Ψ-Hilfer-Prabhakar fractional derivatives and their regularised form, such as the space-time fractional advection-dispersion equation and the generalized fractional free-electron laser (FEL) equation.
Keywords: Ψ-Prabhakar integral, Ψ-Hilfer–Prabhakar derivative, Ψ-Mittag–Leffler function, Ψ-Shehu transform.
Magar, S., Hamoud, A., Khandagale, A., & Ghadle, K. (2023). Generalized Shehu transform to Ψ-Hilfer-Prabhakar fractional derivative and its regularized version. Advances in the Theory of Nonlinear Analysis and Its Application, 6(3), 364–379.