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Fractional Calculus—Theory and Applications, 4th Edition
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Fractional Calculus—Theory and Applications, 4th Edition

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

Deadline for manuscript submissions: 31 October 2026 | Viewed by 1522

Special Issue Editor

Prof. Dr. Jorge E. Macías Díaz

E-Mail Website
Guest Editor
1. Department of Mathematics, School of Digital Technologies, Tallinn University, 10120 Tallinn, Estonia
2. Department of Mathematics and Physics, Autonomous University of Aguascalientes, Aguascalientes 20131, Mexico
Interests: fractional calculus; fractional analysis; numerical methods for fractional differential equations; nonlinear fractional analysis; simulation of fractional systems; nonlinear systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues, 

In recent years, fractional calculus has witnessed tremendous progress in various areas of sciences and mathematics. New definitions of fractional derivatives and integrals have appeared in recent years, extending the classical definitions in some sense or another. Moreover, the rigorous analysis of the functional properties of those new definitions has been an active area of research in mathematical analysis. Systems considering differential equations with fractional-order operators have been investigated rigorously from the analytical and numerical points of view, and potential applications have been proposed in science and technology. The purpose of this Special Issue is to serve as a specialized forum for the dissemination of recent progress in the theory of fractional calculus and its potential applications. We invite authors to submit high-quality reports on the analysis of fractional-order differential/integral equations, the analysis of new definitions of fractional derivatives, numerical methods for fractional-order equations, and applications to physical systems governed by fractional differential equations, among other interesting topics of research.

Prof. Dr. Jorge E. Macías Díaz
Guest Editor

Manuscript Submission Information

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Keywords

  • fractional-order differential/integral equations
  • existence and regularity of solutions
  • numerical methods for fractional equations
  • analysis of convergence and stability
  • applications to science and technology

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Published Papers (1 paper)

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Research

30 pages, 1924 KB  
Article
A Liouville–Caputo Fractional Co-Infection Model: Theoretical Analysis, Ulam-Type Stability, and Numerical Simulation
by Ghaliah Alhamzi, Mona Bin-Asfour, Najat Almutairi, Mansoor Alsulami and Sayed Saber
Axioms 2026, 15(3), 187; https://doi.org/10.3390/axioms15030187 - 4 Mar 2026
Viewed by 549
Abstract
This paper investigates a fractional-order mathematical model for the co-infection dynamics of pneumonia and typhoid fever using the Liouville–Caputo derivative. We establish the existence, uniqueness, non-negativity, and boundedness of solutions using Banach’s fixed point theorem and fractional comparison principles. The Hyers–Ulam and generalized [...] Read more.
This paper investigates a fractional-order mathematical model for the co-infection dynamics of pneumonia and typhoid fever using the Liouville–Caputo derivative. We establish the existence, uniqueness, non-negativity, and boundedness of solutions using Banach’s fixed point theorem and fractional comparison principles. The Hyers–Ulam and generalized Ulam–Hyers–Rassias stability of the system are rigorously proved; this stability analysis is epidemiologically significant because it guarantees that small perturbations in initial conditions or model parameters—inevitable in real-world data collection—do not lead to unbounded deviations in disease trajectory predictions. To approximate solutions numerically, we develop a Laplace-Based Optimized Decomposition Method (LODM) and validate its convergence against a modified predictor–corrector scheme. The LODM provides a semi-analytical series solution, while the predictor–corrector method serves as a numerical benchmark; this dual approach ensures reliability of simulations. Numerical simulations illustrate the influence of the fractional order ξ on system dynamics. Quantitative comparison between ξ=1 (integer order) and ξ<1 (fractional order) demonstrates that fractional modeling reduces peak infection by 12–18% and delays epidemic peaks by 15–30 days, confirming that memory effects capture long-term epidemiological dependencies that integer-order models fail to reproduce. A biological interpretation links the fractional order to immune memory, pathogen persistence, and intervention latency. This study provides both theoretical and numerical evidence supporting the use of fractional calculus in epidemiological modeling. Full article
(This article belongs to the Special Issue Fractional Calculus—Theory and Applications, 4th Edition)
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