New Trends in Fractional Differential Equations with Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C2: Dynamical Systems".

Deadline for manuscript submissions: 31 July 2026 | Viewed by 735

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Center for Research and Training in Innovative Techniques of Applied Mathematics in Engineering, University Politehnica of Bucharest, 060042 Bucharest, Romania
Interests: the application of fractional differential equations in modeling complex systems, with a focus on understanding chaotic dynamics and non-local interactions using fractional calculus
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Special Issue Information

Dear Colleagues,

This Special Issue, titled "New Trends in Fractional Differential Equations with Applications", aims to explore the latest advancements in the theory and applications of fractional differential equations (FDEs). It will focus on emerging methodologies for solving FDEs, including innovative analytical, numerical, and computational approaches. The Special Issue will also examine the growing applications of fractional models across various fields such as physics, engineering, biology, and finance, particularly in modeling complex systems with memory effects and non-local interactions. Furthermore, the Special Issue will delve into the role of fractional calculus in understanding chaotic systems, emphasizing how fractional derivatives provide a more accurate description of chaotic dynamics and long-term behaviors in systems with non-local or historical dependencies. By presenting cutting-edge research, this Special Issue seeks to highlight new trends, foster interdisciplinary collaboration, and stimulate further development in the field of fractional calculus.

Dr. Octavian Postavaru
Guest Editor

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Keywords

  • fractional differential equations
  • fractional calculus
  • chaotic systems
  • applications

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Published Papers (1 paper)

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Research

17 pages, 1025 KB  
Article
A Vectorization Approach to Solving and Controlling Fractional Delay Differential Sylvester Systems
by Fatemah Mofarreh and Ahmed M. Elshenhab
Mathematics 2025, 13(22), 3631; https://doi.org/10.3390/math13223631 - 12 Nov 2025
Viewed by 229
Abstract
This paper addresses the solvability and controllability of fractional delay differential Sylvester matrix equations with non-permutable coefficient matrices. By applying a vectorization approach and Kronecker product algebra, we transform the matrix-valued problem into an equivalent vector system, enabling the derivation of explicit solution [...] Read more.
This paper addresses the solvability and controllability of fractional delay differential Sylvester matrix equations with non-permutable coefficient matrices. By applying a vectorization approach and Kronecker product algebra, we transform the matrix-valued problem into an equivalent vector system, enabling the derivation of explicit solution representations using a delayed perturbation of two-parameter Mittag-Leffler-type matrix functions. We establish necessary and sufficient conditions for controllability via a fractional delay Gramian matrix, providing a computationally verifiable criterion that requires no commutativity assumptions. The theoretical results are validated through numerical examples, demonstrating effectiveness in noncommutative scenarios where classical methods fail. Full article
(This article belongs to the Special Issue New Trends in Fractional Differential Equations with Applications)
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