期刊
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
卷 39, 期 6, 页码 4533-4548出版社
WILEY
DOI: 10.1002/num.22627
关键词
Atangana‐ Baleanu derivative; Caputo‐ Fabrizio derivative; dispersive PDE; Laplace transform
This article investigates fractional dispersive partial differential equations under non-singular and non-local kernels. The Laplace transform is used to obtain the series solution of the equations, and examples are provided to confirm the validity of the proposed scheme.
This article aims to investigate the fractional dispersive partial differential equations (FPDEs) under non-singular and non-local kernels. First, we study the fractional dispersive equations under the Caputo-Fabrizio fractional derivative in one and higher dimension. Second, we investigate the same equations under the Atangana-Baleanu derivative. The Laplace transform has an excellent convergence rate for the exact solution as compared to the other analytical methods. Therefore, we use Laplace transform to obtain the series solution of the proposed equations. We provide two examples of each equation to confirm the validity of the proposed scheme. The results and simulations of examples show higher convergence of the fractional-order solution to the integer-order solution. In the end, we provide the conclusion and physical interpretation of the figures.
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