Fractional Calculus Applied in Environmental Biosystems

A special issue of Fractal and Fractional (ISSN 2504-3110).

Deadline for manuscript submissions: closed (31 October 2025) | Viewed by 1718

Special Issue Editors


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Guest Editor
Department of Statistics, Biostatistics Postgraduate Program (PBE), State University of Maringá, Maringá, Av. Colombo, 5790, Maringá 87020-900, Brazil
Interests: probability; statistics; spatial statistics; geostatistics; applied mathematics; fractional calculus
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Guest Editor
Industrial Engineering Department, Universidade Estadual Do Paraná, R. Comendador Correia Júnior, 117, Paranaguá 83203-560, Brazil
Interests: mathematical modeling; simulation; machine learning; anomalous diffusion; ambipolar diffusivity

Special Issue Information

Dear Colleague,

In recent years, significant strides have been made in the mathematical modeling of environmental biosystems, spanning diverse areas such as complex ecosystems, epidemiology, climate change impact assessment, bioremediation, and ecosystem conservation. These advancements are underpinned by enhanced access to detailed data and refined analytical techniques. Fractional calculus has emerged as a pivotal tool in this progress, offering heightened precision in modeling biological systems. This technique adeptly captures the nonlinear and intricate behaviors exhibited by many biological systems, addressing non-local phenomena and long-memory processes. By adapting to model multiscale phenomena, fractional calculus allows for a more nuanced analysis, particularly in cases involving anomalous behaviors. Essentially, fractional calculus facilitates a deeper and more accurate understanding of biosystems, significantly contributing to advancements in resource management, environmental conservation, and the comprehension of ecosystem dynamics. We invite researchers to submit their original research articles, reviews, and theoretical contributions on the theme of "Fractional Calculus Applied in Environmental Biosystems." Potential topics include, but are not limited to

  • Complex ecosystem models;
  • Dynamic ecological networks;
  • Epidemiological models;
  • Disease spread models;
  • Climate modeling and population impact;
  • Climate change models;
  • Bioremediation and waste treatment;
  • Biological process models;
  • Ecosystem monitoring and conservation;
  • Population dynamics models.

In summary, fractional calculus provides powerful mathematical tools that can be used address the complexity of environmental biosystems. This method not only enhances model accuracy but also enables researchers to explore biological phenomena in more detailed and sophisticated ways, thus significantly contributing to advancements in understanding and managing natural ecosystems.

Dr. Diogo Francisco Rossoni
Dr. Gustavo de Souza Matias
Guest Editors

Manuscript Submission Information

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Keywords

  • bioprocess modeling
  • environmental models
  • biosystem anomalies
  • fractional calculus

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Published Papers (1 paper)

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Research

22 pages, 968 KB  
Article
Fractal–Fractional Coupled Systems with Constant and State- Dependent Delays: Existence Theory and Ecological Applications
by Faten H. Damag, Ashraf A. Qurtam, Arshad Ali, Abdelaziz Elsayed, Alawia Adam, Khaled Aldwoah and Salahedden Omer Ali
Fractal Fract. 2025, 9(10), 652; https://doi.org/10.3390/fractalfract9100652 - 9 Oct 2025
Cited by 1 | Viewed by 859
Abstract
This study introduces a new class of coupled differential systems described by fractal–fractional Caputo derivatives with both constant and state-dependent delays. In contrast to traditional delay differential equations, the proposed framework integrates memory effects and geometric complexity while capturing adaptive feedback delays that [...] Read more.
This study introduces a new class of coupled differential systems described by fractal–fractional Caputo derivatives with both constant and state-dependent delays. In contrast to traditional delay differential equations, the proposed framework integrates memory effects and geometric complexity while capturing adaptive feedback delays that vary with the system’s state. Such a formulation provides a closer representation of biological and physical processes in which delays are not fixed but evolve dynamically. Sufficient conditions for the existence and uniqueness of solutions are established using fixed-point theory, while the stability of the solution is investigated via the Hyers–Ulam (HU) stability approach. To demonstrate applicability, the approach is applied to two illustrative examples, including a predator–prey interaction model. The findings advance the theory of fractional-order systems with mixed delays and offer a rigorous foundation for developing realistic, application-driven dynamical models. Full article
(This article belongs to the Special Issue Fractional Calculus Applied in Environmental Biosystems)
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