Advances in the Theory of Nonlinear Analysis and its Application

Yazarlar: ["Sachın MAGAR", "Ahmed HAMOUD", "Amol KHANDAGALE", "Kirtiwant GHADLE"]

Konular:-

DOI:10.31197/atnaa.1032207

Anahtar Kelimeler:$\Psi$-Prabhakar integral,$\Psi$-Hilfer-Prabhakar derivative,$\Psi$-Mittag-Leffler function,$\Psi$-Shehu transform

Özet: 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.

---