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
Summary
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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Open Access
ARTICLE
Analysis and Numerical Computations of the Multi-Dimensional, Time-Fractional Model of Navier-Stokes Equation with a New Integral Transformation
Yuming Chu, Saima Rashid, Khadija Tul Kubra, Mustafa Inc, Zakia Hammouch, M. S. Osman
Computer Modeling in Engineering & Sciences, Vol.136, No.3, pp. 3025-3060, 2023, DOI:10.32604/cmes.2023.025470
（This article belongs to this Special Issue:
Applications of Fractional Operators in Modeling Real-world Problems: Theory, Computation, and Applications)
Abstract The analytical solution of the multi-dimensional, time-fractional model of Navier-Stokes equation using the triple and quadruple Elzaki transform decomposition method is presented in this article. The aforesaid model is analyzed by employing Caputo fractional derivative. We deliberated three stimulating examples that correspond to the triple and quadruple Elzaki transform decomposition methods, respectively. The findings illustrate that the established approaches are extremely helpful in obtaining exact and approximate solutions to the problems. The exact and estimated solutions are delineated via numerical simulation. The proposed analysis indicates that the projected configuration is extremely meticulous, highly efficient, and precise in understanding the behavior…
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Open Access
ARTICLE
Fractional Order Modeling of Predicting COVID-19 with Isolation and Vaccination Strategies in Morocco
Lakhlifa Sadek, Otmane Sadek, Hamad Talibi Alaoui, Mohammed S. Abdo, Kamal Shah, Thabet Abdeljawad
Computer Modeling in Engineering & Sciences, Vol.136, No.2, pp. 1931-1950, 2023, DOI:10.32604/cmes.2023.025033
（This article belongs to this Special Issue:
Applications of Fractional Operators in Modeling Real-world Problems: Theory, Computation, and Applications)
Abstract In this work, we present a model that uses the fractional order Caputo derivative for the novel Coronavirus disease 2019 (COVID-19) with different hospitalization strategies for severe and mild cases and incorporate an awareness program. We generalize the SEIR model of the spread of COVID-19 with a private focus on the transmissibility of people who are aware of the disease and follow preventative health measures and people who are ignorant of the disease and do not follow preventive health measures. Moreover, individuals with severe, mild symptoms and asymptomatically infected are also considered. The basic reproduction number () and local stability…
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Open Access
ARTICLE
Study of Fractional Order Dynamical System of Viral Infection Disease under Piecewise Derivative
Kamal Shah, Hafsa Naz, Thabet Abdeljawad, Bahaaeldin Abdalla
Computer Modeling in Engineering & Sciences, Vol.136, No.1, pp. 921-941, 2023, DOI:10.32604/cmes.2023.025769
（This article belongs to this Special Issue:
Applications of Fractional Operators in Modeling Real-world Problems: Theory, Computation, and Applications)
Abstract This research aims to understand the fractional order dynamics of the deadly Nipah virus (NiV) disease. We focus on using piecewise derivatives in the context of classical and singular kernels of power operators in the Caputo sense to investigate the crossover behavior of the considered dynamical system. We establish some qualitative results about the existence and uniqueness of the solution to the proposed problem. By utilizing the Newtonian polynomials interpolation technique, we recall a powerful algorithm to interpret the numerical findings for the aforesaid model. Here, we remark that the said viral infection is caused by an
RNA type virus…
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Graphic Abstract
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Open Access
ARTICLE
On Riemann-Type Weighted Fractional Operators and Solutions to Cauchy Problems
Muhammad Samraiz, Muhammad Umer, Thabet Abdeljawad, Saima Naheed, Gauhar Rahman, Kamal Shah
Computer Modeling in Engineering & Sciences, Vol.136, No.1, pp. 901-919, 2023, DOI:10.32604/cmes.2023.024029
（This article belongs to this Special Issue:
Applications of Fractional Operators in Modeling Real-world Problems: Theory, Computation, and Applications)
Abstract In this paper, we establish the new forms of Riemann-type fractional integral and derivative operators. The novel fractional integral operator is proved to be bounded in Lebesgue space and some classical fractional integral and differential operators are obtained as special cases. The properties of new operators like semi-group, inverse and certain others are discussed and its weighted Laplace transform is evaluated. Fractional integro-differential free-electron laser (FEL) and kinetic equations are established. The solutions to these new equations are obtained by using the modified weighted Laplace transform. The Cauchy problem and a growth model are designed as applications along with graphical…
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Open Access
ARTICLE
On the Approximation of Fractal-Fractional Differential Equations Using Numerical Inverse Laplace Transform Methods
Kamran, Siraj Ahmad, Kamal Shah, Thabet Abdeljawad, Bahaaeldin Abdalla
Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2743-2765, 2023, DOI:10.32604/cmes.2023.023705
（This article belongs to this Special Issue:
Applications of Fractional Operators in Modeling Real-world Problems: Theory, Computation, and Applications)
Abstract Laplace transform is one of the powerful tools for solving differential equations in engineering and other science subjects. Using the Laplace transform for solving differential equations, however, sometimes leads to solutions in the Laplace domain that are not readily invertible to the real domain by analytical means. Thus, we need numerical inversion methods to convert the obtained solution from Laplace domain to a real domain. In this paper, we propose a numerical scheme based on Laplace transform and numerical inverse Laplace transform for the approximate solution of fractal-fractional differential equations with order . Our proposed numerical scheme is based on…
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Graphic Abstract
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Open Access
ARTICLE
Modeling Drug Concentration in Blood through Caputo-Fabrizio and Caputo Fractional Derivatives
Muath Awadalla, Kinda Abuasbeh, Yves Yannick Yameni Noupoue, Mohammed S. Abdo
Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2767-2785, 2023, DOI:10.32604/cmes.2023.024036
（This article belongs to this Special Issue:
Applications of Fractional Operators in Modeling Real-world Problems: Theory, Computation, and Applications)
Abstract This study focuses on the dynamics of drug concentration in the blood. In general, the concentration level of a drug
in the blood is evaluated by the mean of an ordinary and first-order differential equation. More precisely, it is solved
through an initial value problem. We proposed a new modeling technique for studying drug concentration in blood
dynamics. This technique is based on two fractional derivatives, namely, Caputo and Caputo-Fabrizio derivatives.
We first provided comprehensive and detailed proof of the existence of at least one solution to the problem; we
later proved the uniqueness of the existing solution. The proof…
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Open Access
ARTICLE
Existence of Approximate Solutions to Nonlinear Lorenz System under Caputo-Fabrizio Derivative
Khursheed J. Ansari, Mustafa Inc, K. H. Mahmoud, Eiman
Computer Modeling in Engineering & Sciences, Vol.135, No.2, pp. 1669-1684, 2023, DOI:10.32604/cmes.2022.022971
（This article belongs to this Special Issue:
Applications of Fractional Operators in Modeling Real-world Problems: Theory, Computation, and Applications)
Abstract In this article, we developed sufficient conditions for the existence and uniqueness of an approximate solution to
a nonlinear system of Lorenz equations under Caputo-Fabrizio fractional order derivative (CFFD). The required
results about the existence and uniqueness of a solution are derived via the fixed point approach due to Banach
and Krassnoselskii. Also, we enriched our work by establishing a stable result based on the Ulam-Hyers (U-H)
concept. Also, the approximate solution is computed by using a hybrid method due to the Laplace transform and
the Adomian decomposition method. We computed a few terms of the required solution through the…
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