Qualitative Study on Semi-Analytical Methods for Solving Nonlinear Time-Fractional Partial Differential Equations (European Journal of Pure and Applied Mathematics, 2025)
This paper focuses on finding Semi-Analytical solutions of nonlinear partial differential equations of fractional order by using four techniques such as Sumudu decomposition, Natural decomposition, Adomian decomposition and modified Laplace variational iteration methods. The fractional derivatives are described in the Caputo sense. In these methods, the solution manifests as a convergent series with conveniently computable components. Numerical results show that the four approaches are easy to implement and accurate when applied to partial differential equations of fractional order, although there are some distinct differences between the methods studied, which depend on the nature of the equations and the conditions associated with them.
Keywords: Nonlinear partial differential equations; Adomian decomposition method; Modified Variational Iteration Laplace Transform Method