New exact solutions of the local fractional modified equal width-Burgers equation on the Cantor sets

IF 3.3 3区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractals-Complex Geometry Patterns and Scaling in Nature and Society Pub Date : 2023-10-17 DOI:10.1142/s0218348x23501116

Kang-Jia Wang

引用次数: 1

Abstract

This study proposes a new fractal modified equal width-Burgers equation (MEWBE) with the local fractional derivative (LFD) for the first time. By defining the Mittag-Leffler function (MLF) on the Cantor set (CS), two special functions, namely, the [Formula: see text] and [Formula: see text] functions, are derived for constructing the auxiliary function to seek the non-differentiable (ND) exact solutions. And 16 groups of the ND exact solutions are successfully established. The solutions on the CS are depicted graphically to interpret the nonlinear dynamic behaviors. Furthermore, the comparative results of the fractal MEWBE and the classical MEWBE are also discussed. The obtained results confirm that the proposed method is effective and powerful, and can provide a promising way to find the ND exact solutions of the local fractional PDEs.

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局部分数阶修正等宽- burgers方程在Cantor集上的新精确解

本文首次提出了一个新的具有局部分数阶导数的分形修正等宽- burgers方程(MEWBE)。通过定义Cantor集(CS)上的Mittag-Leffler函数(MLF)，导出了两个特殊函数，即[公式:见文]和[公式:见文]函数，用于构造辅助函数以求不可微(ND)精确解。成功建立了16组ND精确解。图形化地描述了CS上的解，以解释非线性动力学行为。此外，还讨论了分形MEWBE与经典MEWBE的对比结果。结果表明，该方法是有效的，为寻找局部分数阶偏微分方程的ND精确解提供了一种有希望的方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fractals-Complex Geometry Patterns and Scaling in Nature and Society 数学-数学跨学科应用

CiteScore

7.40

自引率

23.40%

发文量

319

审稿时长

>12 weeks

期刊介绍： The investigation of phenomena involving complex geometry, patterns and scaling has gone through a spectacular development and applications in the past decades. For this relatively short time, geometrical and/or temporal scaling have been shown to represent the common aspects of many processes occurring in an unusually diverse range of fields including physics, mathematics, biology, chemistry, economics, engineering and technology, and human behavior. As a rule, the complex nature of a phenomenon is manifested in the underlying intricate geometry which in most of the cases can be described in terms of objects with non-integer (fractal) dimension. In other cases, the distribution of events in time or various other quantities show specific scaling behavior, thus providing a better understanding of the relevant factors determining the given processes. Using fractal geometry and scaling as a language in the related theoretical, numerical and experimental investigations, it has been possible to get a deeper insight into previously intractable problems. Among many others, a better understanding of growth phenomena, turbulence, iterative functions, colloidal aggregation, biological pattern formation, stock markets and inhomogeneous materials has emerged through the application of such concepts as scale invariance, self-affinity and multifractality. The main challenge of the journal devoted exclusively to the above kinds of phenomena lies in its interdisciplinary nature; it is our commitment to bring together the most recent developments in these fields so that a fruitful interaction of various approaches and scientific views on complex spatial and temporal behaviors in both nature and society could take place.