具有一般记忆效应的分数阶不确定微分方程:存在性与α路径解

IF 2.6 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Modelling and Control Pub Date : 2022-12-31 DOI:10.15388/namc.2023.28.30479

Cheng Luo, Guo-cheng Wu, Lan-Lan Huang

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引用次数: 2

摘要

一般分数微积分是近年来流行的一门学科。提出了一类具有一般记忆效应的分数阶不确定微分方程。首先给出了一般分数阶不确定微分方程解的存在唯一性定理，并给出了一类线性不确定微分方程解的解析解。然后引入了α-路径的概念，并讨论了gude的解与相应α-路径的关系。此外，还证明了求得与GFUDEs解有关的单调函数期望值的一个定理。最后，给出了一个数值例子，以便更好地理解一般记忆效应的重要性。为了更好地描述不确定环境中的某些现象，本文提供了更多类型的模糊函数。

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Fractional uncertain differential equations with general memory effects: Existences and alpha-path solutions

General fractional calculus is popular recently. Fractional uncertain differential equations (FUDEs) with general memory effects are proposed in this paper. Firstly, existence and uniqueness theorems of solution for general fractional uncertain differential equations (GFUDEs) is presented, and the analytic solution of a linear one is given. Then the concept of α-path is introduced, and relationship between solution of GFUDE and corresponding α-path is also discussed. In addition, a theorem is proved to obtain the expected value of a monotonic function related to solutions of GFUDEs. Finally, a numerical example is given to better understand the significance of general memory effects. This paper provides more types of FUDEs to better describe some phenomena in uncertain environments.

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来源期刊

Nonlinear Analysis-Modelling and Control MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

3.80

自引率

10.00%

发文量

审稿时长

9.6 months

期刊介绍： The scope of the journal is to provide a multidisciplinary forum for scientists, researchers and engineers involved in research and design of nonlinear processes and phenomena, including the nonlinear modelling of phenomena of the nature. The journal accepts contributions on nonlinear phenomena and processes in any field of science and technology. The aims of the journal are: to provide a presentation of theoretical results and applications; to cover research results of multidisciplinary interest; to provide fast publishing of quality papers by extensive work of editors and referees; to provide an early access to the information by presenting the complete papers on Internet.