In this paper, a new general double integral transform is introduced. We present its essential properties and proved some useful results such as the double convolution theorem and derivative properties. Furthermore, we apply the proposed double general integral transform to solve some partial differential equations such as telegraph and Klein-Gordon equations.

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.