Fractional Differential Equation and Its Applications, 2nd Edition

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 30 November 2026 | Viewed by 718

Special Issue Editors


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Guest Editor
School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China
Interests: fractional differential equations; stochastic differential equations; impulsive differential equations; stochastic dynamics; stochastic analysis; nonlinear dynamics
Special Issues, Collections and Topics in MDPI journals
School of mathematics and statistics, Northwestern Polytechnical University, Xi'an 710072, China
Interests: applied mathematics; nonlinear dynamics; control; information science; neural network; complex network system
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent years, research on fractional differential equations and their applications has accelerated. In particular, there have been a large number of outstanding achievements in the approximation theory, dynamical behavior, efficient numerical algorithms, complex networks, parameter identification, and other aspects of fractional differential systems, showing a good development trend. Based on this, this Special Issue aims to collect the latest excellent works on the theory, methods, and applications of fractional differential equations.

In this Special Issue, original research articles and reviews are welcome. Research areas may include (but not limited to) the following:

  • Fractional differential equations;
  • Stochastic fractional differential equations;
  • Fractional delay differential equations;
  • Fractional complex networks;
  • Fractional hybrid differential equations;
  • Differential equations driven by fractional Brownian motion;
  • Identification methods for fractional differential systems;
  • Modeling, method and analysis of fractional differential systems;
  • Nonlinear dynamics of fractional differential equations.

We look forward to receiving your valuable contributions.

Dr. Jiankang Liu
Dr. Shuo Zhang
Guest Editors

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Keywords

  • fractional differential equations
  • stability analysis
  • bifurcation
  • chaos
  • and synchronization
  • identification
  • modeling
  • well-posedness
  • fractional brownian motion
  • noise
  • networks
  • delay
  • impulse
  • perturbance

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Published Papers (1 paper)

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Research

15 pages, 561 KB  
Article
Parametric Inequalities for s-Convex Stochastic Processes via Caputo Fractional Derivatives
by Ymnah Alruwaily, Rabab Alzahrani, Fatimah Alshahrani, Badreddine Meftah and Raouf Fakhfakh
Axioms 2026, 15(2), 147; https://doi.org/10.3390/axioms15020147 - 17 Feb 2026
Cited by 1 | Viewed by 398
Abstract
This paper establishes a general parametric integral identity involving (n+1)-times differentiable stochastic processes, formulated entirely in terms of stochastic k-Caputo fractional derivatives. This identity serves as a unifying tool for deriving a broad class of parameter-dependent inequalities [...] Read more.
This paper establishes a general parametric integral identity involving (n+1)-times differentiable stochastic processes, formulated entirely in terms of stochastic k-Caputo fractional derivatives. This identity serves as a unifying tool for deriving a broad class of parameter-dependent inequalities for differentiable s-convex stochastic processes. Remarkably, by assigning specific values to the underlying parameter, we have ensured our results specialize to well-known numerical integration inequalities, including those of midpoint, trapezium, Simpson, and Bullen types, in the stochastic fractional context. The findings not only enrich the theory of stochastic fractional calculus but also provide a flexible analytical apparatus for uncertainty quantification in fractional dynamical systems. Full article
(This article belongs to the Special Issue Fractional Differential Equation and Its Applications, 2nd Edition)
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