A novel homotopy perturbation method with applications to nonlinear fractional order KdV and Burger equation with exponential-decay kernel. (English) Zbl 1475.35380
Summary: 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.
MSC:
| 35R11 | Fractional partial differential equations |
| 35A22 | Transform methods (e.g., integral transforms) applied to PDEs |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
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