Time-fractional Cahn–Allen and time-fractional Klein–Gordon equations: Lie symmetry analysis, explicit solutions and convergence analysis

Abstract

This research analyzes the symmetry analysis, explicit solutions and convergence analysis to the time fractional Cahn–Allen (CA) and time-fractional Klein–Gordon (KG) equations with Riemann–Liouville (RL) derivative. The time fractional CA and time fractional KG are reduced to respective nonlinear ordinary differential equation of fractional order. We solve the reduced fractional ODEs using an explicit power series method. The convergence analysis for the obtained explicit solutions are investigated. Some figures for the obtained explicit solutions are also presented.