Analysis of Fractional Stochastic Differential Equations and Their Applications, Second Edition

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 September 2026 | Viewed by 659

Special Issue Editors


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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
Special Issues, Collections and Topics in MDPI journals

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

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, Second Edition”, 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 250 words) can be sent to the Editorial Office for assessment.

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

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Published Papers (1 paper)

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Research

37 pages, 578 KB  
Article
Moderate Deviation Principle for Two-Time-Scale Caputo FSDEs Driven by Fractional Brownian Motion
by Li Feng, Haibo Gu and Juan Chen
Fractal Fract. 2026, 10(2), 114; https://doi.org/10.3390/fractalfract10020114 - 8 Feb 2026
Viewed by 401
Abstract
This work investigates the moderate deviation principle for a class of two-time-scale Caputo fractional stochastic differential equations. The driving noise of the slow variable is fractional Brownian motion with Hurst index H(12,1). The driving noise [...] Read more.
This work investigates the moderate deviation principle for a class of two-time-scale Caputo fractional stochastic differential equations. The driving noise of the slow variable is fractional Brownian motion with Hurst index H(12,1). The driving noise of the fast variable is standard Brownian motion. The fractional derivative operator of the slow variable is defined by Caputo, and the derivative of the fast variable is of the integer order. The proof process is mainly based on the weak convergence method of fractional Brownian motion variational representation. We first establish the moderate deviation principle by proving the weak convergence of the single-time-scale controlled version. Subsequently, we combine Khasminskii time discretization technology to extend the theoretical framework to two-time-scale systems. Finally, a concrete computational case is offered to demonstrate the applicability of the theoretical framework. Full article
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