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Fractal Fract
Special Issues
Analysis of Fractional Stochastic Differential Equations and Their Applications
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Analysis of Fractional Stochastic Differential Equations and Their Applications

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "General Mathematics, Analysis".

Deadline for manuscript submissions: 30 August 2024 | Viewed by 1060

Special Issue Editors

Prof. Dr. Zhiguo Luo

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China
Interests: fractional differential equations; stochastic differential equations; stability analysis; impulsive differential equations; difference equations and their applications
Dr. Danfeng Luo

E-Mail Website
Guest Editor
Department of Mathematics, Guizhou University, Guiyang 550025, China
Interests: averaging principle in stochastic systems; stability or controllability in fractional differential equations; fuzzy differential equations

Special Issue Information

Dear Colleagues,

The purpose of this Special Issue is to communicate and collect results on fractional stochastic differential equations and their applications. We invite submissions of high-quality articles on the existence, uniqueness, stability, controllability and averaging principle of solutions. This Special Issue, “Analysis of Fractional Stochastic Differential Equations and Their Applications”, focuses on a wide range of topics in fractional stochastic analysis and its applications, including, but not limited to, the following:

  • Finite-time stability
  • Ulam–Hyers stability
  • Controllability
  • Averaging principle
  • Existence or uniqueness
  • Delay differential equations
  • Impulsive differential equations
  • Fuzzy differential equations

Prof. Dr. Zhiguo Luo
Dr. Danfeng Luo
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • fractional differential equations
  • stochastic differential equations
  • delay differential equations
  • impulsive differential equations
  • fuzzy differential equations
  • stability analysis
  • averaging principle
  • controllability
  • averaging principle
  • existence or uniqueness

Published Papers (2 papers)

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Research

15 pages, 315 KiB  
Article
Well-Posedness and Hyers–Ulam Stability of Fractional Stochastic Delay Systems Governed by the Rosenblatt Process
by Ghada AlNemer, Mohamed Hosny, Ramalingam Udhayakumar and Ahmed M. Elshenhab
Fractal Fract. 2024, 8(6), 342; https://doi.org/10.3390/fractalfract8060342 - 6 Jun 2024
Viewed by 428
Abstract
Under the effect of the Rosenblatt process, the well-posedness and Hyers–Ulam stability of nonlinear fractional stochastic delay systems are considered. First, depending on fixed-point theory, the existence and uniqueness of solutions are proven. Next, utilizing the delayed Mittag–Leffler matrix functions and Grönwall’s inequality, [...] Read more.
Under the effect of the Rosenblatt process, the well-posedness and Hyers–Ulam stability of nonlinear fractional stochastic delay systems are considered. First, depending on fixed-point theory, the existence and uniqueness of solutions are proven. Next, utilizing the delayed Mittag–Leffler matrix functions and Grönwall’s inequality, sufficient criteria for Hyers–Ulam stability are established. Ultimately, an example is presented to demonstrate the effectiveness of the obtained findings. Full article
(This article belongs to the Special Issue Analysis of Fractional Stochastic Differential Equations and Their Applications)
23 pages, 640 KiB  
Article
A Fractional Heston-Type Model as a Singular Stochastic Equation Driven by Fractional Brownian Motion
by Marc Mukendi Mpanda
Fractal Fract. 2024, 8(6), 330; https://doi.org/10.3390/fractalfract8060330 - 30 May 2024
Viewed by 236
Abstract
This paper introduces the fractional Heston-type (fHt) model as a stochastic system comprising the stock price process modeled by a geometric Brownian motion. In this model, the infinitesimal return volatility is characterized by the square of a singular stochastic equation driven [...] Read more.
This paper introduces the fractional Heston-type (fHt) model as a stochastic system comprising the stock price process modeled by a geometric Brownian motion. In this model, the infinitesimal return volatility is characterized by the square of a singular stochastic equation driven by a fractional Brownian motion with a Hurst parameter H∈(0,1). We establish the Malliavin differentiability of the fHt model and derive an expression for the expected payoff function, revealing potential discontinuities. Simulation experiments are conducted to illustrate the dynamics of the stock price process and option prices. Full article
(This article belongs to the Special Issue Analysis of Fractional Stochastic Differential Equations and Their Applications)
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