A study of double general transform for solving fractional partial differential equations

Abstract

In this research, we introduce the basic properties of the single and double general transforms. New interesting results related to fractional operators in the sense of Caputo derivative are investigated and proved. In this study, the general double transformation is utilized to study the application on some special functions, such as the Mittag–Leffler function, and on the Caputo's fractional derivative of different and higher orders. Moreover, we establish new interesting formulas and prove some theories that can save efforts and time for researchers as they investigate the properties and applications of integral transformations on fractional operators. The results obtained in this research are tested by solving different types of fractional partial differential equations to obtain exact solutions. The outcomes of this article are valuable to researchers and mathematicians who are interested in the solving fractional partial differential equations via integral transforms, which are considered as important techniques to handle these equations.