A Novel Homotopy Perturbation Method with Applications to Nonlinear Fractional Order KdV and Burger Equation with Exponential-Decay Kernel
Shabir Ahmad, Aman Ullah, Ali Akgül, Manuel De la Sen
Abstract
In this paper, we introduce the Yang transform homotopy perturbation method (YTHPM), which is a novel method. We provide formulae for the Yang transform of Caputo-Fabrizio fractional order derivatives. We derive an algorithm for the solution of Caputo-Fabrizio (CF) fractional order partial differential equation in series form and show its convergence to the exact solution. To demonstrate the novel approach, we include some examples with detailed solutions. We use tables and graphs to compare the exact and approximate solutions.
Topics & Concepts
MathematicsKorteweg–de Vries equationApplied mathematicsHomotopy analysis methodExponential functionHomotopyNonlinear systemHomotopy perturbation methodPartial differential equationPerturbation (astronomy)Fractional calculusKernel (algebra)Mathematical analysisPure mathematicsPhysicsQuantum mechanicsFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsNonlinear Waves and Solitons