@article{article_1032207, title={Generalized Shehu Transform to $\Psi$-Hilfer-Prabhakar Fractional Derivative and its Regularized Version}, journal={Advances in the Theory of Nonlinear Analysis and its Application}, volume={6}, pages={364–379}, year={2022}, DOI={10.31197/atnaa.1032207}, author={Magar, Sachın and Hamoud, Ahmed and Khandagale, Amol and Ghadle, Kirtiwant}, keywords={$\Psi$-Prabhakar integral, $\Psi$-Hilfer-Prabhakar derivative, $\Psi$-Mittag-Leffler function, $\Psi$-Shehu transform}, 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 (FEL) equation.}, number={3}, publisher={Erdal KARAPINAR}