The generalized time-fractional Fornberg–Whitham equation: An analytic approach
Parthkumar P. Sartanpara, Ramakanta Meher, S.K. Meher
Abstract
This work implements a novel analytical approach known as the q-Homotopy Analysis Shehu Transform Method to the time-fractional Fornberg–Whitham equation in Caputo’s sense. The proposed method combines the idea of the q-Homotopy analysis method with the Shehu transform to enhance the efficacy of the proposed method. To demonstrate the correctness of the proposed method, the convergence analysis of the method has been obtained along with its term approximations. Finally, the obtained numerical solution is compared with the available Laplace Adomian decomposition method (LADM) solution and with the exact answer to test the efficiency of the q-HAShTM through the control parameter ħ and n.
Topics & Concepts
Adomian decomposition methodLaplace transformMathematicsHomotopy analysis methodCorrectnessConvergence (economics)Fractional calculusApplied mathematicsLaplace's equationDecomposition method (queueing theory)HomotopyMathematical analysisAlgorithmPartial differential equationPure mathematicsEconomic growthDiscrete mathematicsEconomicsFractional Differential Equations SolutionsNonlinear Waves and SolitonsIterative Methods for Nonlinear Equations