The present article deals with the solution of nonlinear fractional Klein–Fock–Gordon equation which involved the newly developed Caputo–Fabrizio fractional derivative with non-singular kernel. We adopt fractional homotopy perturbation transform method in order to find the approximate solution of fractional Klein–Fock–Gordon equation in the form of rapidly convergent series. Existence and uniqueness analysis of the considered model is provided. We consider few numerical examples to validate the projected technique. The obtained results shows that this method is very efficient, simple in implementation and that it can be applied to solve other nonlinear problems.

本文涉及非线性分数Klein-Fock-Gordon方程的解决方案，该方程涉及新开发的具有非奇异核的Caputo-Fabrizio分数阶导数。为了找到分数Klein-Fock-Gordon方程的快速收敛序列形式的近似解，我们采用分数同伦扰动变换方法。提供了所考虑模型的存在性和唯一性分析。我们考虑了几个数值示例来验证所提出的技术。所得结果表明，该方法非常有效，实现简单，可用于解决其他非线性问题。