On Time Fractional Partial Differential Equations and Their Solution by Certain Formable Transform Decomposition Method

This paper aims to investigate a new efficient method for solving time fractional partial differential equations. In this orientation, a reliable formable transform decomposition method has been designed and developed, which is a novel combination of the formable integral transform and the decomposition method. Basically, certain accurate solutions for time-fractional partial differential equations have been presented. The method under concern demands more simple calculations and fewer efforts compared to the existing methods. Besides, the posed formable transform decomposition method has been utilized to yield a series solution for given fractional partial differential equations. Moreover, several interesting formulas relevant to the formable integral transform are applied to fractional operators which are performed as an excellent application to the existing theory. Furthermore, the formable transform decomposition method has been employed for finding a series solution to a time-fractional Klein-Gordon equation. Over and above, some numerical simulations are also provided to ensure reliability and accuracy of the new approach.