A GENERALIZED METHOD AND ITS APPLICATIONS TO n-DIMENSIONAL FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS IN FRACTAL DOMAIN

Chao Yue, Wen-Xiu Ma and Kun Li
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Chao Yue: School of Economy, Shandong Women’s University, Jinan 250300, P. R. China
Wen-Xiu Ma: ��Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA§Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia¶College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, P. R. China∥International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa
Kun Li: ��College of Medical Information Engineering, Shandong First Medical University & Shandong, Academy of Medical Sciences, Taian 271000, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 03, 1-12

Abstract: A generalized local fractional Riccati differential equation (LFRDE) method, which is a combination of the local fractional Riccati differential equation method and the transformed rational function approach, is presented to obtain the non-differentiable exact traveling wave solutions for n-dimensional fractional partial differential equations. In order to verify the effectiveness of the method, the seventh-order local fractional Sawada–Kotera–Ito equation, the local fractional sine-Gordon equation and the local fractional Kadomtsev–Petviashvili equation in fractal domain are first considered. The obtained results show that the presented method involving fractal special functions, are powerful and effective for obtaining exact solutions of nonlinear fractional partial differential equations in fractal domains.

Keywords: Traveling Wave Solution; Generalized LFRDE; Fractional Partial Differential Equation; Fractal (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22500712

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