Fractal and Fractional · 2022 · 10 citations · 35 references
Natural SciencesMathematicsComputational Fluid DynamicsDerivativesDifferential EquationsIterative SolversNumerical AlgorithmsNumerical ConvergenceNumerical Methods For Differential EquationsPartial Differential EquationsPerturbation MethodsConvergent SequencesDifferential Equation FormulationDifferential Equation SolversDiffusion EquationFractional Differential EquationsFuzzy Differential EquationsNonlinear Partial Differential EquationsVariational Methods In Partial Differential Equations
In this article, the authors study the comparison of the generalization differential transform method (DTM) and fuzzy variational iteration method (VIM) applied to determining the approximate analytic solutions of fuzzy fractional KdV, K(2,2) and mKdV equations. Furthermore, we establish the approximation solution two-and three-dimensional fuzzy time-fractional telegraphic equations via the fuzzy reduced differential transform method (RDTM). Finding an exact or closed-approximation solution to a differential equation is possible via fuzzy RDTM. Finally, we present the fuzzy fractional variational homotopy perturbation iteration method (VHPIM) with a modified Riemann-Liouville derivative to solve the fuzzy fractional diffusion equation (FDE). Using this approach achieves a rapidly convergent sequence that approaches the exact solution of the equation. The proposed methods are investigated based on fuzzy fractional derivatives with some illustrative examples. The results reveal that the schemes are highly effective for obtaining the solutions to fuzzy fractional partial differential equations.
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Homotopy perturbation technique
Ji‐Huan He · Computer Methods in Applied Mechanics and Engineering · 1999 · 3.5K citations
Madan L. Puri, Dan A. Ralescu · Journal of Mathematical Analysis and Applications · 1986 · 1.9K citations