Applications of Fractional Calculus in Modern Mathematical Modeling
A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Numerical and Computational Methods".
Deadline for manuscript submissions: 31 December 2025 | Viewed by 83
Special Issue Editors
2. Center for Research in Mathematics and Applications (CIMA), Institute for Advanced Studies and Research (IIFA), University of Évora, Rua Romão Ramalho, 59, 7000-671 Évora, Portugal
Interests: differential and difference equations; dynamical systems; boundary value problems; topological and variational methods; fractional calculus; differential and integral equations
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2. Department of Physical Sciences, The University of Chenab, Gujrat, Pakistan
Interests: complex nonlinear stochastic dynamical systems; reduce-order models; machine learning; data assimilation; stochastic methods; numerical analysis of stochastic models; fractional calculus; differential and integral equations
Special Issues, Collections and Topics in MDPI journals
Interests: computational biology; numerical analysis; non-linear dynamics; stochastic differential equations; stochastic methods
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
Fractional calculus extends the notion of derivatives and integrals of arbitrary order and gives rise to a variety of complex models and analyzes. This is due to its ability to capture the effects of memory and many other effects that other forms of calculus simply cannot capture. Therefore, this Special Issue will aggregate the latest research that focuses on the most recent theoretical advances, computing methods, and wide applications of fractional calculus in the modern mathematical modeling of various fields such as physics, biology, engineering, and finance. It will be centered around the theory of fractional calculus, new analytical and numerical methods for solving fractional differential equations, fractional partial differential equations and their applications, the biological modeling of fractional calculus, control systems and engineering, the application of fractional differential calculus to financial and economic problems, the mathematics of fractional calculus methods, non-local operators in mathematical modeling, the epidemiology and treatment of infectious diseases, and the use of fractional operators and models of time-fractional derivatives.
Prof. Dr. Feliz Manuel Minhós
Dr. Ali Raza
Dr. Muhammad Mohsin
Guest Editors
Manuscript Submission Information
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Keywords
- fractional calculus
- fractional differential equations (FDEs)
- fractional delay differential equations (FDDEs)
- stochastic fractional delay differential equations (SFDDEs)
- memory effects
- fractional partial differential equations (FRDE's)
- stochastic fractional partial differential equations (SFPDEs)
- existence and uniqueness of solutions for FDEs
- stability analysis of FDEs
- sufficient conditions for solvability of FDEs with multi-point type data
- uniqueness of solution for FDEs with impulses given by functions with several variables
- solvability of functional FDES in involving P-Laplacian
- multiplicity results for singular FDES in biological models
- numerical methods in fractional calculus
- biological systems modeling through fractional calculus
- efficient computational methods to solve fractional differential equations for biological systems
- control theory
- mathematical modeling in finance through fractional calculus
- data-driven approaches through fractional calculus
- machine learning with fractional operators
- future research directions and open problems in the application of fractional calculus in mathematical modeling
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