A Novel Homotopy Perturbation Method with Applications to Nonlinear Fractional Order KdV and Burger Equation with Exponential-Decay Kernel
Author(s) -
Shabir Ahmad,
Aman Ullah,
Ali Akgül,
Manuel De la Sen
Publication year - 2021
Publication title -
journal of function spaces
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.579
H-Index - 28
eISSN - 2314-8896
pISSN - 2314-8888
DOI - 10.1155/2021/8770488
Subject(s) - mathematics , korteweg–de vries equation , homotopy analysis method , exponential function , homotopy , nonlinear system , homotopy perturbation method , partial differential equation , perturbation (astronomy) , fractional calculus , kernel (algebra) , mathematical analysis , pure mathematics , physics , quantum mechanics
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.
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