Abstract
In this work, four well known time Fractional Partial Differential Equations (FPDEs) namely, time Fractional Fornberg-Whitham
Equation (FFWE), time Fractional KdV Equation (FKdVE), time Fractional Convection-Diffusion Equation (FCDE) and time Fractional BBMBurger Equation (FBBMBE) are solved numerically through Fractional
Wave Variable Transformation (FWVT) and Successive Differentiation
Method (SDM). By using the FWVT, ζ = λx −
vtα
Γ(α + 1), these FPDEs
are converted into an Ordinary Differential Equation (ODE). Then SDM is
applied on thus formed ODE to produce their Taylor series. A comparison
of obtained numerical series at α = 1 with the exact solution is presented
to prove the accuracy of this technique as well as graphical illustrations
for different values of α. SDM along with fractional wave variable transformation proves to be an adequate and accurate method for obtaining
numerical solutions of FPDEs.
M. Khalid, Mariam Sultana, Fareeha Sami Khan. (2020) A Modernistic Approach to Handle Time Fractional Partial Differential Equations by Merging Successive Differentiation Method and Fractional Wave Variable Transformation, Punjab University Journal of Mathematics, Volume 52 , Issue No.3.
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