Query：
学者姓名：章红梅
Refining：
Year
Type
Indexed by
Source
Complex
Former Name
Co-
Language
Clean All
Abstract ：
The pioneering work in finance by Black, Scholes and Merton during the 1970s led to the emergence of the Black-Scholes (B-S) equation, which offers a concise and transparent formula for determining the theoretical price of an option. The establishment of the B-S equation, however, relies on a set of rigorous assumptions that give rise to several limitations. The non-local property of the fractional derivative (FD) and the identification of fractal characteristics in financial markets have paved the way for the introduction and rapid development of fractional calculus in finance. In comparison to the classical B-S equation, the fractional B-S equations (FBSEs) offer a more flexible representation of market behavior by incorporating long-range dependence, heavy-tailed and leptokurtic distributions, as well as multifractality. This enables better modeling of extreme events and complex market phenomena, The fractional B-S equations can more accurately depict the price fluctuations in actual financial markets, thereby providing a more reliable basis for derivative pricing and risk management. This paper aims to offer a comprehensive review of various FBSEs for pricing European options, including associated solution techniques. It contributes to a deeper understanding of financial model development and its practical implications, thereby assisting researchers in making informed decisions about the most suitable approach for their needs.
Keyword ：
analytic solution analytic solution European option European option fractional Black-Scholes equation fractional Black-Scholes equation fractional derivative fractional derivative numerical simulation numerical simulation
Cite：
Copy from the list or Export to your reference management。
| GB/T 7714 | Zhang, Hongmei , Zhang, Mengchen , Liu, Fawang et al. Review of the Fractional Black-Scholes Equations and Their Solution Techniques [J]. | FRACTAL AND FRACTIONAL , 2024 , 8 (2) . |
| MLA | Zhang, Hongmei et al. "Review of the Fractional Black-Scholes Equations and Their Solution Techniques" . | FRACTAL AND FRACTIONAL 8 . 2 (2024) . |
| APA | Zhang, Hongmei , Zhang, Mengchen , Liu, Fawang , Shen, Ming . Review of the Fractional Black-Scholes Equations and Their Solution Techniques . | FRACTAL AND FRACTIONAL , 2024 , 8 (2) . |
| Export to | NoteExpress RIS BibTex |
Version ：
Abstract ：
This paper introduces fractional Brownian motion into the study of Maxwell nanofluids over a stretching surface. Nonlinear coupled spatial fractional-order energy and mass equations are established and solved numerically by the finite difference method with Newton's iterative technique. The quantities of physical interest are graphically presented and discussed in detail. It is found that the modified model with fractional Brownian motion is more capable of explaining the thermal conductivity enhancement. The results indicate that a reduction in the fractional parameter leads to thinner thermal and concentration boundary layers, accompanied by higher local Nusselt and Sherwood numbers. Consequently, the introduction of a fractional Brownian model not only enriches our comprehension of the thermal conductivity enhancement phenomenon but also amplifies the efficacy of heat and mass transfer within Maxwell nanofluids. This achievement demonstrates practical application potential in optimizing the efficiency of fluid heating and cooling processes, underscoring its importance in the realm of thermal management and energy conservation.
Keyword ：
fractional Brownian motion fractional Brownian motion improved Buongiorno model improved Buongiorno model Maxwell nanofluids Maxwell nanofluids Riemann-Liouville fractional derivative Riemann-Liouville fractional derivative
Cite：
Copy from the list or Export to your reference management。
| GB/T 7714 | Shen, Ming , Liu, Yihong , Yin, Qingan et al. Enhanced Thermal and Mass Diffusion in Maxwell Nanofluid: A Fractional Brownian Motion Model [J]. | FRACTAL AND FRACTIONAL , 2024 , 8 (8) . |
| MLA | Shen, Ming et al. "Enhanced Thermal and Mass Diffusion in Maxwell Nanofluid: A Fractional Brownian Motion Model" . | FRACTAL AND FRACTIONAL 8 . 8 (2024) . |
| APA | Shen, Ming , Liu, Yihong , Yin, Qingan , Zhang, Hongmei , Chen, Hui . Enhanced Thermal and Mass Diffusion in Maxwell Nanofluid: A Fractional Brownian Motion Model . | FRACTAL AND FRACTIONAL , 2024 , 8 (8) . |
| Export to | NoteExpress RIS BibTex |
Version ：
Abstract ：
The present study delves into the significance of Cattaneo-Christov double diffusion and the induced magnetic field (IMF) on a stagnation-point flow of Maxwell ternary nanofluids. A new boundary condition with the magnetic response is designed to study superior heat and mass transfer of Maxwell ternary nanofluid combined with double diffusion and IMF. The governing equations are formulated by mathematically modeling of the current flow in a Cartesian coordinate system and solved using an improved shooting method and the RungeKutta method. Through the application of similarity transformations, the governing equations are transformed into a system of initial boundary value ordinary differential equations. These equations are further transformed into linear equations with initial value problems using the shooting method and subsequently solved using the Runge-Kutta method and Newton's iterative techniques. The numerical results and correlation analysis vividly demonstrate the profound influence of double diffusion and IMF on thermal and concentration patterns via graphical representations. It is found that the double diffusion and the induced magnetic field always helps to achieve lower temperature and concentration. The magnetic response boundary leads to higher heat and mass transfer efficiency for the suction case. The magnetically responsive boundary is verified to be effective for regulating the heat and mass transfer of ternary nanofluid.
Keyword ：
Cattaneo-Christov double diffusion Cattaneo-Christov double diffusion Induced magnetic field Induced magnetic field Magnetic response boundary Magnetic response boundary Multiple regression analysis Multiple regression analysis Ternary nanofluid Ternary nanofluid
Cite：
Copy from the list or Export to your reference management。
| GB/T 7714 | Chen, Hui , Ma, Yiren , Shen, Ming et al. Significance of Cattaneo-Christov double diffusion and induced magnetic field on Maxwell ternary nanofluid flow with magnetic response boundary [J]. | JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS , 2023 , 587 . |
| MLA | Chen, Hui et al. "Significance of Cattaneo-Christov double diffusion and induced magnetic field on Maxwell ternary nanofluid flow with magnetic response boundary" . | JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS 587 (2023) . |
| APA | Chen, Hui , Ma, Yiren , Shen, Ming , He, Panfeng , Zhang, Hongmei . Significance of Cattaneo-Christov double diffusion and induced magnetic field on Maxwell ternary nanofluid flow with magnetic response boundary . | JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS , 2023 , 587 . |
| Export to | NoteExpress RIS BibTex |
Version ：
Abstract ：
基于多项式样条函数,提出一种求解具有非线性源项的双侧空间分数阶扩散方程的数值方法.通过傅里叶分析证明了所提出的数值方法是无条件稳定和收敛的.为了验证所构造差分格式的有效性,引入分数阶行方法(MOL)与之进行比较.最后给出数值例子,并验证数值结果与理论分析是相吻合的.
Keyword ：
二次多项式样条函数 二次多项式样条函数 分数阶扩散方程 分数阶扩散方程 收敛性 收敛性 稳定性 稳定性 行方法 行方法 非线性源项 非线性源项
Cite：
Copy from the list or Export to your reference management。
| GB/T 7714 | 陈雪娟 , 陈景华 , 章红梅 . 求解具有非线性源项的双侧空间分数阶扩散方程的样条方法 [J]. | 厦门大学学报(自然科学版) , 2021 , 60 (06) : 981-988 . |
| MLA | 陈雪娟 et al. "求解具有非线性源项的双侧空间分数阶扩散方程的样条方法" . | 厦门大学学报(自然科学版) 60 . 06 (2021) : 981-988 . |
| APA | 陈雪娟 , 陈景华 , 章红梅 . 求解具有非线性源项的双侧空间分数阶扩散方程的样条方法 . | 厦门大学学报(自然科学版) , 2021 , 60 (06) , 981-988 . |
| Export to | NoteExpress RIS BibTex |
Version ：
Abstract ：
基于高等数学教学过程中出现的种种问题,文章以精准教学理念为切入点,从教学内容、教学方法、教学评价等方面对电类专业的高等数学实施精准教学改革,以实现教学效果的最优化.精准教学改革举措包括:编写对接专业的教材、设计匹配专业的教案、提供适应专业的专题复习;以兴趣为导向,激发学生学习的热情;多样化的教学方法体现学生的主体地位;多元化的评价推进精准教学改革.最后通过实践验证精准教学实施的显著效果.
Keyword ：
主体地位 主体地位 数学思维 数学思维 电类高等数学 电类高等数学 精准教学 精准教学
Cite：
Copy from the list or Export to your reference management。
| GB/T 7714 | 周燕 , 周勇 , 吕书龙 et al. 电类专业高等数学精准教学的实践探索 [J]. | 高等理科教育 , 2020 , (5) : 117-123 . |
| MLA | 周燕 et al. "电类专业高等数学精准教学的实践探索" . | 高等理科教育 5 (2020) : 117-123 . |
| APA | 周燕 , 周勇 , 吕书龙 , 刘文丽 , 任立英 , 章红梅 . 电类专业高等数学精准教学的实践探索 . | 高等理科教育 , 2020 , (5) , 117-123 . |
| Export to | NoteExpress RIS BibTex |
Version ：
Abstract ：
讨论一个二维调和分数阶扩散方程,其中的调和分数阶导数是分数阶导数的推广,可模拟粒子在早期的超扩散向后期的次扩散的渐进行为.采用隐式交替方向法(ADI)和Crank-Nicolson(C-N)格式建立方程的数值离散格式,并采用外推法得到差分格式的二阶精度,运用矩阵分析的方法给出稳定性和收敛性的证明,同时给出一个数值例子说明所建立的数值离散格式的有效性.
Keyword ：
Crank-Nicolson格式 Crank-Nicolson格式 调和分数阶导数 调和分数阶导数 隐式交替方向法 隐式交替方向法
Cite：
Copy from the list or Export to your reference management。
| GB/T 7714 | 陈景华 , 陈雪娟 , 章红梅 . 二维调和分数阶扩散方程的数值模拟 [J]. | 厦门大学学报(自然科学版) , 2019 , 58 (06) : 882-888 . |
| MLA | 陈景华 et al. "二维调和分数阶扩散方程的数值模拟" . | 厦门大学学报(自然科学版) 58 . 06 (2019) : 882-888 . |
| APA | 陈景华 , 陈雪娟 , 章红梅 . 二维调和分数阶扩散方程的数值模拟 . | 厦门大学学报(自然科学版) , 2019 , 58 (06) , 882-888 . |
| Export to | NoteExpress RIS BibTex |
Version ：
Abstract ：
提出两类高维多项时间分数阶偏微分方程的模型,此模型可用来描述广义黏弹性Oldroyd-B流体的剪应力和剪切速率之间的非线性关系.采用分离变量法将此分数阶偏微分方程转化成分数阶常微分方程,从而得到此高维多项时间分数阶偏微分方程的解析解,解的形式以多重Mittag-Leffler函数的形式给出.
Keyword ：
分离变量法 分离变量法 多重Mittag-Leffler函数 多重Mittag-Leffler函数 多项时间分数阶偏微分方程 多项时间分数阶偏微分方程 广义Oldroyd-B流体 广义Oldroyd-B流体
Cite：
Copy from the list or Export to your reference management。
| GB/T 7714 | 陈景华 , 陈雪娟 , 章红梅 . 基于广义Oldroyd-B流体问题的高维多项时间分数阶偏微分方程的解析解 [J]. | 厦门大学学报(自然科学版) , 2019 , 58 (03) : 397-401 . |
| MLA | 陈景华 et al. "基于广义Oldroyd-B流体问题的高维多项时间分数阶偏微分方程的解析解" . | 厦门大学学报(自然科学版) 58 . 03 (2019) : 397-401 . |
| APA | 陈景华 , 陈雪娟 , 章红梅 . 基于广义Oldroyd-B流体问题的高维多项时间分数阶偏微分方程的解析解 . | 厦门大学学报(自然科学版) , 2019 , 58 (03) , 397-401 . |
| Export to | NoteExpress RIS BibTex |
Version ：
Abstract ：
为了克服旧课程体系与改革开放以后大学数学教学总学时数日益减少的尖锐矛盾,顺应现代化教育理念的发展趋势,我们利用近代数学的观点和方法,统筹重组电类、信息类专业大学数学基础课的教学内容,形成新的课程体系,并借助多样化的教学模式和现代化的教育手段,更深刻地向学生揭示数学知识的本质,培养学生的数学思维和创造创新能力.
Keyword ：
专业导向 专业导向 信息技术 信息技术 大学数学 大学数学 教学改革 教学改革
Cite：
Copy from the list or Export to your reference management。
| GB/T 7714 | 章红梅 , 周燕 , 程航 et al. 新时期大学数学课程改革的探索和实践 [J]. | 海峡科学 , 2019 , (6) : 79-80,91 . |
| MLA | 章红梅 et al. "新时期大学数学课程改革的探索和实践" . | 海峡科学 6 (2019) : 79-80,91 . |
| APA | 章红梅 , 周燕 , 程航 , 刘文丽 . 新时期大学数学课程改革的探索和实践 . | 海峡科学 , 2019 , (6) , 79-80,91 . |
| Export to | NoteExpress RIS BibTex |
Version ：
Abstract ：
A new time and spatial fractional heat conduction model with Brownian diffusion and thermophoresis is presented to investigate the heat and mass transfer of Maxwell viscoelastic nanofluid over a moving flat plate in porous medium. New dimensionless variables are introduced to nondimensionalize the governing equations which are solved numerically by L1 algorithm and shifted Grunwald formula. The main observations of the model are the effects of embedded time and space fractional parameters on velocity, temperature and concentration profiles which are analyzed graphically. Numerical computations for a comparison between the heat conduction model with the time and spatial fractional derivatives and the model with spatial fractional derivative are made. It is found that the heat transfer is enhanced by the time and spatial fractional heat conduction model. Moreover, the larger fractional derivatives refer to the stronger memory characteristic which exhibits the physical meanings of fractional derivative. (C) 2019 Elsevier Ltd. All rights reserved.
Keyword ：
Brownian diffusion and thermophoresis Brownian diffusion and thermophoresis Heat and mass transfer Heat and mass transfer Maxwell viscoelastic nanofluid Maxwell viscoelastic nanofluid Time and spatial fractional derivatives Time and spatial fractional derivatives
Cite：
Copy from the list or Export to your reference management。
| GB/T 7714 | Zhang, Mengchen , Shen, Ming , Liu, Fawang et al. A new time and spatial fractional heat conduction model for Maxwell nanofluid in porous medium [J]. | COMPUTERS & MATHEMATICS WITH APPLICATIONS , 2019 , 78 (5) : 1621-1636 . |
| MLA | Zhang, Mengchen et al. "A new time and spatial fractional heat conduction model for Maxwell nanofluid in porous medium" . | COMPUTERS & MATHEMATICS WITH APPLICATIONS 78 . 5 (2019) : 1621-1636 . |
| APA | Zhang, Mengchen , Shen, Ming , Liu, Fawang , Zhang, Hongmei . A new time and spatial fractional heat conduction model for Maxwell nanofluid in porous medium . | COMPUTERS & MATHEMATICS WITH APPLICATIONS , 2019 , 78 (5) , 1621-1636 . |
| Export to | NoteExpress RIS BibTex |
Version ：
Abstract ：
When the fluctuation of option price is regarded as a fractal transmission system and the stock price follows a Levy distribution, a time-space fractional option pricing model (TSFOPM) is obtained. Then we discuss the numerical simulation of the TSFOPM. A discrete implicit numerical scheme with a second-order accuracy in space and a 2 - gamma order accuracy in time is constructed, where gamma is a transmission exponent. The stability and convergence of the obtained numerical scheme are analyzed. Moreover, a fast bi-conjugate gradient stabilized method is proposed to solve the numerical scheme in order to reduce the storage space and computational cost. Then a numerical example with exact solution is presented to demonstrate the accuracy and effectiveness of the proposed numerical method. Finally, the TSFOPM and the above numerical technique are applied to price European call option. The characteristics of the fractional option pricing model are analyzed in comparison with the classical Black-Scholes (B-S) model. (C) 2018 Elsevier Inc. All rights reserved.
Keyword ：
Caputo fractional derivative Caputo fractional derivative European call option European call option Fast numerical simulation Fast numerical simulation Modified Riemann-Liouville fractional derivative Modified Riemann-Liouville fractional derivative Time-space fractional option pricing model Time-space fractional option pricing model
Cite：
Copy from the list or Export to your reference management。
| GB/T 7714 | Zhang, H. , Liu, F. , Chen, S. et al. Fast numerical simulation of a new time-space fractional option pricing model governing European call option [J]. | APPLIED MATHEMATICS AND COMPUTATION , 2018 , 339 : 186-198 . |
| MLA | Zhang, H. et al. "Fast numerical simulation of a new time-space fractional option pricing model governing European call option" . | APPLIED MATHEMATICS AND COMPUTATION 339 (2018) : 186-198 . |
| APA | Zhang, H. , Liu, F. , Chen, S. , Anh, V , Chen, J. . Fast numerical simulation of a new time-space fractional option pricing model governing European call option . | APPLIED MATHEMATICS AND COMPUTATION , 2018 , 339 , 186-198 . |
| Export to | NoteExpress RIS BibTex |
Version ：
Export
| Results： |
Selected to |
| Format： |
