An efficient technique for nonlinear time-fractional Klein–Fock–Gordon equation

摘要

In this article, the q-homotopy analysis transform method(q-HATM) is hired to find the solution for the time-fractional Klein–Fock–Gordon (FKFG) equation. The FKFG equation plays an important role in describing the relativistic electrons. To ensure the applicability and efficiency of proposed algorithm, we consider three cases of nonlinear FKFG equation. The uniqueness and convergence analysis for the projected problem is presented with the aid of Banach's fixed point theory. The numerical simulation has been presented to confirm the reliability and proficiency of the proposed scheme. Moreover, the behaviour of the obtained solution has been captured for diverse fractional order. The obtained results elucidate that, the proposed technique is easy to implement and very effective to analyse the behaviour complex problems arise in science and technology.