Abstract
Abstract The basic motivation of the present study is to extend the application of the local fractional Yang-Laplace decomposition method to solve nonlinear systems of local fractional partial differential equations. The differential operators are taken in the local fractional sense. The local fractional Yang-Laplace decomposition method (LFLDM) can be easily applied to many problems and is capable of reducing the size of computational work to find non-differentiable solutions for similar problems. Two illustrative examples are given, revealing the effectiveness and convenience of the method.
Highlights
Fractional partial differential equations is a fundamental tool for the analysis of physical phenomena, such as, electromagnetic, acoustics, viscoelasticity, electrochemistry, and others
Djelloul Ziane et al Applied Mathematics and Nonlinear Sciences 4(2019) 489–502 are expressed by fractional partial differential equations, which have been solved by several numerical-analytical methods ( [13], [21], [25])
With the new concepts of fractional derivative and fractional integral, as well as local fractional derivative and local fractional integral, researchers were able to use the Adomian decomposition method (ADM) method to solve these new types of equations or systems which include, local fractional differential equations, local fractional partial differential equations and local fractional integro-differential equations ( [6]- [10])
Summary
Fractional partial differential equations is a fundamental tool for the analysis of physical phenomena, such as, electromagnetic, acoustics, viscoelasticity, electrochemistry, and others. Some more results were obtained by combining fractional differential operators with some known transforms, such as the Young-Laplace transform method and the Sumudu transform method, obtaining a solution of fractional equations or systems, even in the nonlinear case. Among these works we find the local fractional Laplace decomposition method [11] and the local fractional Sumudu decomposition method ( [12], [14]). Based on the concept of local fractional operator and on the Yang-Laplace decomposition method, Jassim has recently proposed a method [11] to solve linear local fractional partial differential equations.
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