A Modernistic Approach to Handle Time Fractional Partial Differential Equations by Merging Successive Differentiation Method and Fractional Wave Variable Transformation

In this work, four well known time Fractional Partial Dif-ferential Equations (FPDEs) namely, time Fractional Fornberg-WhithamEquation (FFWE), time Fractional KdV Equation (FKdVE), time Frac-tional Convection-Diffusion Equation (FCDE) and time Fractional BBM-Burger Equation (FBBMBE) are solved numerically through FractionalWave Variable Transformation (FWVT) and Successive DifferentiationMethod (SDM). By using the FWVT,ζ=λx−vtαΓ(α+ 1), these FPDEsare converted into an Ordinary Differential Equation (ODE). Then SDM isapplied on thus formed ODE to produce their Taylor series. A comparisonof obtained numerical series atα= 1with the exact solution is presentedto prove the accuracy of this technique as well as graphical illustrationsfor different values ofα. SDM along with fractional wave variable trans-formation proves to be an adequate and accurate method for obtainingnumerical solutions of FPDE