Table of Content

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

Submission Deadline: 31 December 2022 (closed) Submit to Special Issue

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


  • Open Access

    ARTICLE

    Study of Fractional Order Dynamical System of Viral Infection Disease under Piecewise Derivative

    Kamal Shah, Hafsa Naz, Thabet Abdeljawad, Bahaaeldin Abdalla
    CMES-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… More >

    Graphic Abstract

    Study of Fractional Order Dynamical System of Viral Infection Disease under Piecewise Derivative

  • 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
    CMES-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… More >

  • 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
    CMES-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… More >

    Graphic Abstract

    On the Approximation of Fractal-Fractional Differential Equations Using Numerical Inverse Laplace Transform Methods

  • 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
    CMES-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… More >

  • Open Access

    ARTICLE

    Existence of Approximate Solutions to Nonlinear Lorenz System under Caputo-Fabrizio Derivative

    Khursheed J. Ansari, Mustafa Inc, K. H. Mahmoud, Eiman
    CMES-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… More >

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