Exact and numerical solutions of higher-order fractional partial differential equations: A new analytical method and some applications

In this paper, the solution methodology of higher-order linear fractional partial deferential equations (FPDEs) as mentioned in eqs (1) and (2) below Caputo definition relies on a new analytical method which is called Laplace-residual power series (L-RPSM). The main idea our proposed technique to convert original FPDE Laplace space, then apply residual (RPSM) by using concept limit obtain solution. Some interesting important numerical test applications are given discussed illustrate procedure method, also confirm that simple, understandable very fast for obtaining exact approximate solutions (ASs) FPDEs compared with other methods such RPSM, variational iteration (VIM), homotopy perturbation (HPM) Adomian decomposition (ADM). advantage its simplicity computing coefficients terms only at infinity not well-known as, RPSM need derivative (FD) each time determine unknown solutions, VIM, ADM, or HPM integration operators difficult case.