Towards new general double integral transform and its applications to differential equations

Abstract

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.

A Generalized Approach of Triple Integral Transforms and Applications

“…Tis transform is important due to its ability in generalizing large numbers of single transforms. Recently, Meddahi and others [38] introduced a new general double integral transform that generalizes the idea of double transforms, that is given for a continuous function of two variables as…”

Fareeha transform: A new generalized Laplace transform

“…In this paper, the author proved that every integral transform is actually a special case of its generalized integral transform and solved various examples of differential equation, integral equations, and fractional integral equations. Also, they wrote another paper [9] in which the double integral transformation have been proven for solving the partial differential equations.…”

Solving Partial Integro-Differential Equations via Double Formable Transform

“…Te double integral transforms have drawn researchers' attention recently because of their contribution to the solution of equations involving two variables and fnding precise solutions in the simplest ways possible. However, with the development of science and the urgent need for mathematics to solve newly emerged problems, it was necessary to pay attention to scientists and researchers to obtain new and advanced methods to keep speed with these problems [12][13][14]. Te most popular double integral transforms that are used to solve partial diferential equations are the double Laplace transform [15,16], the double Laplace-Sumudu transform [17], the double Sumudu transform [18], the ARA-Sumudu transform [19,20], the double Shehu transform [21], the double Elzaki transform [12], and others [22].…”

“…In 2021, with the advent of the formable integral transform (FT) that was presented by Saadah and Ghazal [24], its ability to solve ordinary, partial diferential equations, and integral equations, and its properties that could enable us to solve a wide kind of diferential and integral problems, we intend to defne the new double formable transform. Moreover, it is worth mentioning here that the formable transform might be considered a special case of the new integral transform presented by Jafari in [25], and the idea of double integral transforms is also generalized by the authors in [14]. Te main advantage of using the double formable transform is that it preserves the values of constants, which simplifes the calculations during the solving of problems, and it transforms the target problem from twodimensional space into four-dimensional space.…”