New general single, double and triple conformable integral transforms: Definitions, properties and applications

Abstract

This study introduces an innovative general adaptive integral transform in single, double and triple types. This article outlines the definitions of these new transformations and establishes their main characteristics in each species. In addition, it examines the connections between newly introduced generic transformations and existing transformations. It is shown that previously developed adaptive transforms, including Laplace, Sumodo, Elzaki, G-transforms, Pourreza, and Aboodh, appear as special cases of this general adaptive transform. Furthermore, the effectiveness of the conformal generalized transform is demonstrated through its application in solving different types of linear and nonlinear fractional differential equations. Such as Black–Scholes and Berger’s equations, to demonstrating its proficiency in this domain. The proposed approach demonstrates versatility by encompassing nearly all conformable integral transforms of orders one, two, and three. As a result, it eliminates the need to derive new formulas for single, double, and triple conformable integral transforms, streamlining the process and enhancing the efficiency of solving related problems.

Keywords

• Conformable integral transform
• Conformable derivative
• Integral transforms
• Fractional Klein–Gordon equation