New general integral transform via Atangana–Baleanu derivatives

Abstract

The current paper is about the investigation of a new integral transform introduced recently by Jafari. Specifically, we explore the applicability of this integral transform on Atangana–Baleanu derivative and the associated fractional integral. It is shown that by applying specific conditions on this integral transform, other integral transforms are deduced. We provide examples to reinforce the applicability of this new integral transform.

Generalized Formal integral transform on Ψ-Hilfer-Prabhakar fractional derivatives and its applications

“…Proof. By using the Ψ-Formable transform definition on Ψ-Prabhakar fractional derivative (6) and equations ( 29), (35) we get…”

Ulam–Hyers Stability of Linear Differential Equation with General Transform

“…In [23], the authors employed both the Haar wavelets collocation method and the Homotopy perturbation general transform technique. In [24], the authors proposed the Atangana-Baleanu-Caputo fractional derivative operator in the generalized integral transform sense.…”

New generalized integral transform on Hilfer-Prabhakar fractional derivatives and its applications

“…In 2021, a new integral transform was introduced by Jafari.H in [4], recently which has been used by Meddahi and Jafari in their paper [5] through Atangana-Baleanu fractional derivative and they obtained the existing sub cases such as Laplace, Elzaki, Sumudu and Shehu transforms on Atangana-Baleanu derivatives. This new transform, known as the new generalized integral transform, encompasses a wide range of integral transforms including those in the Laplace transform family, and it is particularly useful in solving differential equations and integral equations.…”