Numerical solutions of nonlinear time fractional Klein-Gordon equation via natural transform decomposition method and iterative Shehu transform method

Abstract

The time-fractional Klein-Gordon equation was analyzed in this article using the natural transform decomposition method (NTDM) and the iterative Shehu transform method (ISTM) with a singular kernel derivative. We employed natural transform (NT) and Shehu transform (ST), followed by inverse natural transform and inverse Shehu transform respectively, to obtain the solution. The numerical simulations are provided to ensure that the methods under consideration are efficient. The current framework captures the behaviour of the obtained findings for various fractional orders. The findings of this study indicate that the proposed methods are effective and reliable in analyzing fractional differential equations.