Exact solutions of φ-Hilfer time-fractional partial differential equations

In this article, we employ the invariant subspace method to systematically and analytically solve the ψ -Hilfer time-fractional PDEs (tFPDEs). More precisely, this work explains how the exact solutions of linear and nonlinear ψ-Hilfer tFPDEs can be obtained with the help of the invariant solution spaces of homogeneous linear ordinary differential equations (HLODEs). Also, different kinds of exact solutions are explicitly computed for the ψ -Hilfer tFPDEs. In addition, we illustrate the dependence of the derived exact solutions on the function ψ( t ), the arbitrary-order parameter α and the type β through graphical demonstrations.