Table of Content

Advanced Numerical Methods for Fractional Differential Equations

Submission Deadline: 15 September 2022 (closed)

Guest Editors

Prof. Qasem M. Al-Mdallal, UAE University, UAE
Prof. Thabet Abdeljawad, Prince Sultan University, Saudi Arabia
Prof. Fahd Jarad, Çankaya University, Turkey

Summary

Fractional calculus, which is defined by the branch of calculus that generalizes the derivative of a function to non-integer order, is born in 1695 in a letter written by Gottfried Wilhelm Leibniz to Guillaume de l'Hôspital. Later, more great scientists contributed to the development of the field of fractional operators such as: Liouville, Riemann, and Laurent. Additionally, several theoretical studies on fractional calculus were reported in the 19th century.

 

In recent years, the area of Fractional Calculus received a huge interest from the scientific community especially mathematicians, physicians, and engineers. This interest is due to the usage of fractional calculus in the mathematical modeling of systems with memory effects. Consequently, the importance of fractional calculus appears in many applications in various fields such as biology, chemistry, networks, fractal geometry, fluid dynamics, control theory, medicine, and finance, etc. 

 

The main target of this special issue is to create a multidisciplinary forum of discussions on the most recent results in this field of research. More precisely, we will focus on recent advanced numerical studies on Fractional Differential. In addition, the well-developed analysis of existing numerical algorithms in terms of efficiency, applicability, convergence, stability and accuracy is of importance. A discussion of nontrivial numerical examples is encouraged.

 

Potential topics include, but are not limited to:

 

•     Numerical methods for Fractional differential equations.

•     Numerical methods for Fractional difference equations.

•     Numerical methods for Fractional integro-differential equations.

•     Mathematical control theory.

•     Any Related topics




Published Papers


  • Open Access

    ARTICLE

    The Fractional Investigation of Some Nonlinear Partial Differential Equations by Using an Efficient Procedure

    Fairouz Tchier, Hassan Khan, Shahbaz Khan, Poom Kumam, Ioannis Dassios
    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2137-2153, 2023, DOI:10.32604/cmes.2023.022855
    (This article belongs to this Special Issue: Advanced Numerical Methods for Fractional Differential Equations)
    Abstract The nonlinearity in many problems occurs because of the complexity of the given physical phenomena. The present paper investigates the non-linear fractional partial differential equations’ solutions using the Caputo operator with Laplace residual power series method. It is found that the present technique has a direct and simple implementation to solve the targeted problems. The comparison of the obtained solutions has been done with actual solutions to the problems. The fractional-order solutions are presented and considered to be the focal point of this research article. The results of the proposed technique are highly accurate and provide useful information about the… More >

  • Open Access

    ARTICLE

    A Detailed Mathematical Analysis of the Vaccination Model for COVID-19

    Abeer S. Alnahdi, Mdi B. Jeelani, Hanan A. Wahash, Mansour A. Abdulwasaa
    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.2, pp. 1315-1343, 2023, DOI:10.32604/cmes.2022.023694
    (This article belongs to this Special Issue: Advanced Numerical Methods for Fractional Differential Equations)
    Abstract This study aims to structure and evaluate a new COVID-19 model which predicts vaccination effect in the Kingdom of Saudi Arabia (KSA) under Atangana-Baleanu-Caputo (ABC) fractional derivatives. On the statistical aspect, we analyze the collected statistical data of fully vaccinated people from June 01, 2021, to February 15, 2022. Then we apply the Eviews program to find the best model for predicting the vaccination against this pandemic, based on daily series data from February 16, 2022, to April 15, 2022. The results of data analysis show that the appropriate model is autoregressive integrated moving average ARIMA (1, 1, 2), and… More >

  • Open Access

    ARTICLE

    A Theoretical Investigation of the SARS-CoV-2 Model via Fractional Order Epidemiological Model

    Tahir Khan, Rahman Ullah, Thabet Abdeljawad, Manar A. Alqudah, Faizullah Faiz
    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.2, pp. 1295-1313, 2023, DOI:10.32604/cmes.2022.022177
    (This article belongs to this Special Issue: Advanced Numerical Methods for Fractional Differential Equations)
    Abstract We propose a theoretical study investigating the spread of the novel coronavirus (COVID-19) reported in Wuhan City of China in 2019. We develop a mathematical model based on the novel corona virus's characteristics and then use fractional calculus to fractionalize it. Various fractional order epidemic models have been formulated and analyzed using a number of iterative and numerical approaches while the complications arise due to singular kernel. We use the well-known Caputo-Fabrizio operator for the purposes of fictionalization because this operator is based on the non-singular kernel. Moreover, to analyze the existence and uniqueness, we will use the well-known fixed… More >

  • Open Access

    ARTICLE

    Numerical Solutions of Fractional Variable Order Differential Equations via Using Shifted Legendre Polynomials

    Kamal Shah, Hafsa Naz, Thabet Abdeljawad, Aziz Khan, Manar A. Alqudah
    CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.2, pp. 941-955, 2023, DOI:10.32604/cmes.2022.021483
    (This article belongs to this Special Issue: Advanced Numerical Methods for Fractional Differential Equations)
    Abstract In this manuscript, an algorithm for the computation of numerical solutions to some variable order fractional differential equations (FDEs) subject to the boundary and initial conditions is developed. We use shifted Legendre polynomials for the required numerical algorithm to develop some operational matrices. Further, operational matrices are constructed using variable order differentiation and integration. We are finding the operational matrices of variable order differentiation and integration by omitting the discretization of data. With the help of aforesaid matrices, considered FDEs are converted to algebraic equations of Sylvester type. Finally, the algebraic equations we get are solved with the help of… More >

  • Open Access

    ARTICLE

    Exact Solutions and Finite Time Stability of Linear Conformable Fractional Systems with Pure Delay

    Ahmed M. Elshenhab, Xingtao Wang, Fatemah Mofarreh, Omar Bazighifan
    CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.2, pp. 927-940, 2023, DOI:10.32604/cmes.2022.021512
    (This article belongs to this Special Issue: Advanced Numerical Methods for Fractional Differential Equations)
    Abstract We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay. By using new conformable delayed matrix functions and the method of variation, we obtain a representation of their solutions. As an application, we derive a finite time stability result using the representation of solutions and a norm estimation of the conformable delayed matrix functions. The obtained results are new, and they extend and improve some existing ones. Finally, an example is presented to illustrate the validity of our theoretical results. More >

  • Open Access

    ARTICLE

    Regarding Deeper Properties of the Fractional Order Kundu-Eckhaus Equation and Massive Thirring Model

    Yaya Wang, P. Veeresha, D. G. Prakasha, Haci Mehmet Baskonus, Wei Gao
    CMES-Computer Modeling in Engineering & Sciences, Vol.133, No.3, pp. 697-717, 2022, DOI:10.32604/cmes.2022.021865
    (This article belongs to this Special Issue: Advanced Numerical Methods for Fractional Differential Equations)
    Abstract In this paper, the fractional natural decomposition method (FNDM) is employed to find the solution for the KunduEckhaus equation and coupled fractional differential equations describing the massive Thirring model. The massive Thirring model consists of a system of two nonlinear complex differential equations, and it plays a dynamic role in quantum field theory. The fractional derivative is considered in the Caputo sense, and the projected algorithm is a graceful mixture of Adomian decomposition scheme with natural transform technique. In order to illustrate and validate the efficiency of the future technique, we analyzed projected phenomena in terms of fractional order. Moreover,… More >

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