Representation of exact solutions of ψ-fractional nonlinear evolution equations using two different approaches

Abstract

In this paper, we investigate the applicability of the separation of variables method (SVM) and the invariant subspace method (ISM) for getting exact solutions of variable coefficients nonlinear fractional partial differential equations with ψ -Riemann–Liouville (RL) fractional derivative. For certain cases of the variable coefficients, the exact separable solutions for two variable coefficients nonlinear evolution equations with ψ − RL fractional derivative are obtained. The obtained results show that the two methods used in this paper are very effective in investigating the exact solutions of evolution equations with ψ − R L fractional derivative.