具有时间相关系数的时间分数 Black-Scholes 方程的分组分类

IF 2.5 2区数学 Q1 MATHEMATICS

Fractional Calculus and Applied Analysis Pub Date : 2024-09-16 DOI:10.1007/s13540-024-00339-4

Jicheng Yu, Yuqiang Feng

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引用次数: 0

摘要

本文提出了具有时间相关系数的时间分数 Black-Scholes 方程的李对称性分析。通过研究随时间变化的系数 $\sigma(t)$、r(t) 和 s(t) 进行组分类。然后利用得到的组生成器对所研究的方程进行还原，其中一些还原方程是带有 Erdélyi-Kober 分数导数的分数普通方程，并构造了一些精确解，包括幂级数解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

$Group classification of time fractional Black-Scholes equation with time-dependent coefficients$

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Group classification of time fractional Black-Scholes equation with time-dependent coefficients

In this paper, we present Lie symmetry analysis for time fractional Black-Scholes equation with time-dependent coefficients. The group classification is carried out by investigating the time-dependent coefficients $\sigma (t)$, r(t) and s(t). Then the obtained group generators are used to reduce the equation under study, some of the reduced equations are fractional ordinary equations with Erdélyi-Kober fractional derivative, and some exact solutions including power series solutions are constructed.

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来源期刊

Fractional Calculus and Applied Analysis MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

16.70%

发文量

101

期刊介绍： Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.