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
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Open Access
ARTICLE
A Study on the Nonlinear Caputo-Type Snakebite Envenoming Model with Memory
Pushpendra Kumar, Vedat Suat Erturk, V. Govindaraj, Dumitru Baleanu
CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.3, pp. 2487-2506, 2023, DOI:10.32604/cmes.2023.026009
（This article belongs to this Special Issue:
Advanced Numerical Methods for Fractional Differential Equations)
Abstract In this article, we introduce a nonlinear Caputo-type snakebite envenoming model with memory. The well-known Caputo fractional derivative is used to generalize the previously presented integer-order model into a fractional-order sense. The numerical solution of the model is derived from a novel implementation of a finite-difference predictor-corrector (L1-PC) scheme with error estimation and stability analysis. The proof of the existence and positivity of the solution is given by using the fixed point theory. From the necessary simulations, we justify that the first-time implementation of the proposed method on an epidemic model shows that the scheme is fully suitable and time-efficient…
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Open Access
ARTICLE
On Nonlinear Conformable Fractional Order Dynamical System via Differential Transform Method
Kamal Shah, Thabet Abdeljawad, Fahd Jarad, Qasem Al-Mdallal
CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.2, pp. 1457-1472, 2023, DOI:10.32604/cmes.2023.021523
（This article belongs to this Special Issue:
Advanced Numerical Methods for Fractional Differential Equations)
Abstract This article studies a nonlinear fractional order Lotka-Volterra prey-predator type dynamical system. For the proposed study, we consider the model under the conformable fractional order derivative (CFOD). We investigate the mentioned dynamical system for the existence and uniqueness of at least one solution. Indeed, Schauder and Banach fixed point theorems are utilized to prove our claim. Further, an algorithm for the approximate analytical solution to the proposed problem has been established. In this regard, the conformable fractional differential transform (CFDT) technique is used to compute the required results in the form of a series. Using Matlab-16, we simulate the series…
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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…
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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…
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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…
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Open Access
ARTICLE
On Fuzzy Conformable Double Laplace Transform with Applications to Partial Differential Equations
Thabet Abdeljawad, Awais Younus, Manar A. Alqudah, Usama Atta
CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.3, pp. 2163-2191, 2023, DOI:10.32604/cmes.2022.020915
（This article belongs to this Special Issue:
Advanced Numerical Methods for Fractional Differential Equations)
Abstract The Laplace transformation is a very important integral transform, and it is extensively used in solving ordinary differential equations, partial differential equations, and several types of integro-differential equations. Our purpose in this study is to introduce the notion of fuzzy double Laplace transform, fuzzy conformable double Laplace transform (FCDLT). We discuss some basic properties of FCDLT. We obtain the solutions of fuzzy partial differential equations (both one-dimensional and two-dimensional cases) through the double Laplace approach. We demonstrate through numerical examples that our proposed method is very successful and convenient for resolving partial differential equations.
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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…
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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.
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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,…
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