Analysis and Applications of Fractional Calculus and Mathematical Modelling

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

Deadline for manuscript submissions: 31 March 2025 | Viewed by 1161

Special Issue Editor


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Departamento de Engenharia Química, Universidade Federal do Paraná, Rua Coronel Francisco H. dos Santos, 100, Curitiba 81531-980, PR, Brazil
Interests: fractional calculus; process control; process instrumentation; diffusion phenomena; design of experiments
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Special Issue Information

 Dear Colleagues,

Almost 330 years after Leibniz’s letter to L'Hopital, fractional calculus and derivatives of arbitrary order are still being used extensively and widely in both fundamental and applied research. Consequently, it is important to consider the following question:

How far can knowledge and scientific boundaries be pushed with the aid of fractional calculus?

This Special Issue, entitled “Analysis and Applications of Fractional Calculus and Mathematical Modelling”, intends to provide readers with state-of-the-art research publications showing ideas and challenges for future research and contribute to the beginning of collaboration and exchange among different research groups in fractional calculus worldwide in the future.

To achieve this goal, the Special Issue has two major branches. In the first one, manuscripts with fundamental research involving analytical mathematical methods, novel derivative definitions, and numerical methods for faster solutions, among others, are very welcome. In the second branch, applied research studies and scenarios will certainly aid in the development of a milestone Special Issue by investigating fractional calculus' applications to different research areas and fields, such as process systems engineering, transport phenomena, biological systems, electrical circuits, and materials science, among others.

From these two branches—fundamental and applied research—this Special Issue intends to become a valuable reference for both beginners and senior researchers in the academic world and also for practitioner professionals in industry.

Dr. Marcelo Kaminski Lenzi
Guest Editor

Manuscript Submission Information

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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 calculus
  • fractional differential and integral equations
  • fractional models
  • mathematical modelling
  • fractional dynamics
  • modeling simulation
  • process control
  • application of fractional calculus, focusing on modeling and optimization.

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Published Papers (1 paper)

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Research

23 pages, 9619 KiB  
Article
Global Mittag-Leffler Attractive Sets, Boundedness, and Finite-Time Stabilization in Novel Chaotic 4D Supply Chain Models with Fractional Order Form
by Muhamad Deni Johansyah, Aceng Sambas, Muhammad Farman, Sundarapandian Vaidyanathan, Song Zheng, Bob Foster and Monika Hidayanti
Fractal Fract. 2024, 8(8), 462; https://doi.org/10.3390/fractalfract8080462 - 6 Aug 2024
Viewed by 871
Abstract
This research explores the complex dynamics of a Novel Four-Dimensional Fractional Supply Chain System (NFDFSCS) that integrates a quadratic interaction term involving the actual demand of customers and the inventory level of distributors. The introduction of the quadratic term results in significantly larger [...] Read more.
This research explores the complex dynamics of a Novel Four-Dimensional Fractional Supply Chain System (NFDFSCS) that integrates a quadratic interaction term involving the actual demand of customers and the inventory level of distributors. The introduction of the quadratic term results in significantly larger maximal Lyapunov exponents (MLE) compared to the original model, indicating increased system complexity. The existence, uniqueness, and Ulam–Hyers stability of the proposed system are verified. Additionally, we establish the global Mittag-Leffler attractive set (MLAS) and Mittag-Leffler positive invariant set (MLPIS) for the system. Numerical simulations and MATLAB phase portraits demonstrate the chaotic nature of the proposed system. Furthermore, a dynamical analysis achieves verification via the Lyapunov exponents, a bifurcation diagram, a 0–1 test, and a complexity analysis. A new numerical approximation method is proposed to solve non-linear fractional differential equations, utilizing fractional differentiation with a non-singular and non-local kernel. These numerical simulations illustrate the primary findings, showing that both external and internal factors can accelerate the process. Furthermore, a robust control scheme is designed to stabilize the system in finite time, effectively suppressing chaotic behaviors. The theoretical findings are supported by the numerical results, highlighting the effectiveness of the control strategy and its potential application in real-world supply chain management (SCM). Full article
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