Approximate Solution of Nonlinear Time-Fractional Klein-Gordon Equations Using Yang Transform

Abstract

The algebras of the symmetry operators for the Klein–Gordon equation are important for a charged test particle, moving in an external electromagnetic field in a space time manifold on the isotropic hydrosulphate. In this paper, we develop an analytical and numerical approach for providing the solution to a class of linear and nonlinear fractional Klein–Gordon equations arising in classical relativistic and quantum mechanics. We study the Yang homotopy perturbation transform method (YHPTM), which is associated with the Yang transform (YT) and the homotopy perturbation method (HPM), where the fractional derivative is taken in a Caputo–Fabrizio (CF) sense. This technique provides the solution very accurately and efficiently in the form of a series with easily computable coefficients. The behavior of the approximate series solution for different fractional-order ℘ values has been shown graphically. Our numerical investigations indicate that YHPTM is a simple and powerful mathematical tool to deal with the complexity of such problems.