ADAMS–BASHFORTH NUMERICAL METHOD-BASED SOLUTION OF FRACTIONAL ORDER FINANCIAL CHAOTIC MODEL

IF 3.3 3区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractals-Complex Geometry Patterns and Scaling in Nature and Society Pub Date : 2023-08-22 DOI:10.1142/s0218348x23500871

R. M. Jena, S. Chakraverty, Shengda Zeng, V. T. Nguyen

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引用次数: 0

Abstract

A new definition of fractional differentiation of nonlocal and non-singular kernels has recently been developed to overcome the shortcomings of the traditional Riemann–Liouville and Caputo fractional derivatives. In this study, the dynamic behaviors of the fractional financial chaotic model have been investigated. Singular and non-singular kernel fractional derivatives are used to examine the proposed model. To solve the financial chaotic model with nonlocal operators, the fractional Adams–Bashforth method (ABM) is applied based on Lagrange polynomial interpolation (LPI). The existence and uniqueness of the solution of the model can be demonstrated using fixed point theory and nonlinear analysis. Further, the error analysis of the present method and Ulam–Hyers stability of the considered model have also been included. Obtained numerical simulations reveal that the model based on three different fractional derivatives shows various chaotic behaviors that may be useful in a practical sense which may not be observed in the integer case.

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基于Adams-bashforth数值方法的分数阶金融混沌模型解

为了克服传统Riemann-Liouville和Caputo分数阶导数的缺点，最近提出了非局部和非奇异核分数阶微分的新定义。本文研究了分数阶金融混沌模型的动力学行为。利用奇异核分数阶导数和非奇异核分数阶导数对模型进行检验。为了求解具有非局部算子的金融混沌模型，采用了基于拉格朗日多项式插值的分数阶Adams-Bashforth方法。利用不动点理论和非线性分析证明了模型解的存在唯一性。此外，还包括了本方法的误差分析和所考虑模型的Ulam-Hyers稳定性。得到的数值模拟结果表明，基于三种不同分数阶导数的模型显示出各种混沌行为，这些行为在实际意义上可能是有用的，而在整数情况下可能没有观察到。

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.