Dual-wave solutions for the quadratic–cubic conformable-caputo time-fractional klein–fock–gordon equation

Abstract

In this paper, the conformable-time-fractional Klein–Fock–Gordon equation is considered and solved using the Kudryashov-expansion method to extract dual-wave solutions. Only, the quadratic and the cubic cases of the model are investigated. It has been noticed that physical changes in the construction of the obtained solutions are reported in the case of transition from the quadratic-state into the cubic-state. Additionally, the Caputo-time-fractional quadratic–cubic Klein–Fock–Gordon is also considered and studied by implementing the residual power series method. A comparison between these two types of fractional derivatives is discussed and the 2D–3D plots are provided to support the findings of this work.