An Efficient Analytical Method for Analyzing the Nonlinear Fractional Klein–Fock–Gordon Equations

The purpose of this article is to solve a nonlinear fractional Klein–Fock–Gordon equation that involves a recently created non-singular kernel fractional derivative by Caputo–Fabrizio. Motivated by some physical applications related to the fractional Klein–Fock–Gordon equation, we focus our study on this equation and some phenomena rated to it. The findings are crucial and essential for explaining a variety of physical processes. In order to find satisfactory approximations to the offered problems, this work takes into account a modern methodology and fractional operator in this context. We first take the Yang transform of the Caputo–Fabrizio fractional derivative and then implement it to solve fractional Klein–Fock–Gordon equations. We will consider three cases of the nonlinear fractional Klein–Fock–Gordon equation to ensure the applicability and effectiveness of the suggested technique. In order to determine an approximate solution to the fractional Klein–Fock–Gordon equation in the fast convergent series form, we can use the fractional homotopy perturbation transform approach. The numerical simulation is provided to demonstrate the effectiveness and dependability of the suggested method. Furthermore, several fractional orders will be used to describe the behavior of the given solutions. The results achieved demonstrate the high efficiency, ease of use, and applicability of this strategy for resolving other nonlinear issues.