Extended least square homotopy method for solving nonlinear systems of fractional partial differential equations

Several methods have been developed to solve fractional Partial Differential Equations (PDEs), most of which provide approximate solutions. Exact analytical solutions, however, are important for the proper understanding of the qualitative features of the concerned phenomena and processes. This paper introduces new effective, analytical, and computational extensions of the least square homotopy method (LSHM) for solving nonlinear systems of fractional PDEs. Moreover, the convergence theorem of the solution is also shown. A significant result of the proposed method is that this method yields exact solutions for some models of space-time fractional PDEs. The Graphical representations of solutions are also shown.