Advances in the Research on Solutions of Impulsive Differential Equations

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C1: Difference and Differential Equations".

Deadline for manuscript submissions: 31 January 2026 | Viewed by 778

Special Issue Editors


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Guest Editor
College of Mathematics, Hunan University, Changsha 410012, China
Interests: impulsive differential equation; stochastic differential equation; optimization problem; fractional differential equation
Special Issues, Collections and Topics in MDPI journals
Department of Mathematics, Wilfrid Laurier University, Waterloo, ON N2L 3C5, Canada
Interests: biomathematics; evolutionary game theory; nonlinear dynamics; differential equations
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

(Random) Impulsive differential equations have received considerable attention because they fully consider the impact of instantaneous sudden phenomena on a system state and accurately reflect the changing laws of things; however, the presence of impulses makes the study of dynamic theory more complex. In the past few decades, the development of nonlinear analysis (fixed-point theory, variational analysis) has provided certain theoretical methods for impulsive differential equations, but there are still many problems that have not been solved. On the other hand, impulses also have great value in application fields, such as control. Impulsive control has the advantages of low cost and precise control, and is widely used. We created this Special Issue to address these issues.

This Special Issue aims to encourage high-quality manuscript submissions, highlighting innovative methods and applications for studying the qualitative theories of impulsive differential equations.

Dr. Xiao-Bao Shu
Dr. Fei Xu
Guest Editors

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Keywords

  • impulsive dynamic system
  • (random) impulsive differential equations
  • stability theory
  • existence theory
  • optimal control
  • bifurcation and chaos
  • random dynamic system
  • stochastic dynamic system

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Published Papers (1 paper)

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Research

21 pages, 358 KiB  
Article
Peano Theorems for Pedjeu–Ladde-Type Multi-Time Scale Stochastic Differential Equations Driven by Fractional Noises
by Arcady Ponosov and Lev Idels
Mathematics 2025, 13(2), 204; https://doi.org/10.3390/math13020204 - 9 Jan 2025
Viewed by 505
Abstract
This paper examines fractional multi-time scale stochastic functional differential equations that, in addition, are driven by fractional noises. Based on a specially crafted fixed-point principle for the so-called “local operators”, we prove a Peano-type theorem on the existence of weak solutions, that is, [...] Read more.
This paper examines fractional multi-time scale stochastic functional differential equations that, in addition, are driven by fractional noises. Based on a specially crafted fixed-point principle for the so-called “local operators”, we prove a Peano-type theorem on the existence of weak solutions, that is, those defined on an extended stochastic basis. To encompass all commonly used particular classes of fractional multi-time scale stochastic models, including those with random delays and impulses at random times, we consider equations with nonlinear random Volterra operators rather than functions. Some crucial properties of the associated integral operators, needed for the proofs of the main results, are studied as well. To illustrate major findings, several existence theorems, generalizing those known in the literature, are offered, with the emphasis put on the most popular examples such as ordinary stochastic differential equations driven by fractional noises, fractional stochastic differential equations with variable delays and fractional stochastic neutral differential equations. Full article
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