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Applications of Fractional Operators in Modeling Real-world Problems: Theory, Computation, and Applications

Submission Deadline: 31 December 2022 (closed)

Guest Editors

Dr. Ndolane Sene, Cheikh Anta Diop University, Dakar Fann, Senegal
Prof. Mehmet Yavuz, University of Exeter, UK
Prof. MUSTAFA İNÇ, Firat University, Turkey


Fractional calculus has grown many papers this last decade and can be applied in many domains as chaos theory, physics, mathematical physics, sciences and engineering, and many other fields. The fractional calculus attraction is due to the diversity of fractional operators. Many operators exist in fractional calculus as Caputo derivative, Riemann-Liouville derivative, Conformable derivative, Caputo-Fabrizio derivative, Atangana-Baleanu derivative, and many others operators. In mathematics and physics literature, fractional operators can be used in modeling diffusion equations with reaction and without reaction terms, modeling electrical circuits, modeling epidemic models, modeling fluids models, and finding solutions to fractional stokes problems. Modeling with fractional operators has attracted many researchers due to the heredity and the memory of the fractional operators. One of the main applications of the fractional operators is that it is noticed that fractional operators generate new types of diffusion as the sub-diffusion, a new type of biological models, new problems of control, and synchronizations, new stability notions, and new types of chaotic systems, and others.


This issue will be devoted to collecting works in modeling mathematical physics models using fractional operators with and without singular kernels. Nowadays, many types of fractional differential equations exist, and methods to solve them have been opened in fractional calculus. We can cite homotopy methods, Fourier and Laplace transform methods, predictor-corrector method, implicit and explicit numerical schemes, adaptative controls, synchronization problems, etc. Therefore, this special issue will be an arena to focus on modeling real-world problems with fractional operators. The papers with applications in mathematical physics and computations are encouraged. Biological models with computations belong to the complexity domain, thus modeling epidemic model with fractional operators are encouraged in the present issue. Another interest will be to propose the existence and uniqueness of the fractional differential equations, the numerical and analytical methods for solving fractional differential equations. One of the main applications of fractional operators in mathematical physics is the modeling diffusion processes. As mentioned in the literature, many diffusion processes exist as sub-diffusion, super-diffusion, hyper-diffusion, and ballistic diffusion. All the previously cited diffusion processes correspond to specific values of the fractional operators. Thus, for papers in physics and mathematical physics, including fractional operators, the authors are strongly encouraged to propose new methods for solving fractional diffusion equations with or without reaction.


Potential topics include but are not limited to the following:

1) Analytical methods for getting solutions to the fractional differential equations.

2) Numerical methods for fractional differential equations.

3) Modeling fluid and nanofluid models using fractional operators.

4) Modeling epidemic models using fractional operators.

5) Solution for the fractional diffusion equations with and without reaction terms.

6) Optimal control and stability analysis.

7) Modeling fluids model using integer and fractional operators.

8) Applications of fractional calculus in physics and mathematical physics.

9) Existence and uniqueness of the solution of the fractional differential equations.

10) Stability criterion and synchronizations in fractional calculus.

Published Papers

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