Muhammad Farman^1,2,4, Ali Akgül^3,9,*, Mir Sajjad Hashemi⁵, Liliana Guran^6,7, Amelia Bucur^8,*

CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.2, pp. 1385-1403, 2024, DOI:10.32604/cmes.2023.028803

Abstract New fractional operators, the COVID-19 model has been studied in this paper. By using different numerical techniques and the time fractional parameters, the mechanical characteristics of the fractional order model are identified. The uniqueness and existence have been established. The model’s Ulam-Hyers stability analysis has been found. In order to justify the theoretical results, numerical simulations are carried out for the presented method in the range of fractional order to show the implications of fractional and fractal orders. We applied very effective numerical techniques to obtain the solutions of the model and simulations. Also, we present conditions of existence for… More >

Muhammad Samraiz¹, Muhammad Umer¹, Thabet Abdeljawad^2,3,*, Saima Naheed¹, Gauhar Rahman⁴, Kamal Shah^2,5

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.1, pp. 901-919, 2023, DOI:10.32604/cmes.2023.024029

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 >

Fouad A. Abolaban^*

CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.1, pp. 183-201, 2021, DOI:10.32604/cmes.2021.015472

Abstract Various epidemics have occurred throughout history, which has led to the investigation and understanding of their transmission dynamics. As a result, non-local operators are used for mathematical modeling in this study. Therefore, this research focuses on developing a dysentery diarrhea model with the use of a fractional operator using a one-parameter Mittag–Leffler kernel. The model consists of three classes of the human population, whereas the fourth one belongs to the pathogen population. The model carefully deals with the dimensional homogeneity among the parameters and the fractional operator. In addition, the model was validated by fitting the actual number of dysentery… More >

Saima Rashid¹, Zakia Hammouch², Rehana Ashraf³, Yu-Ming Chu^4,*

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.1, pp. 359-378, 2021, DOI:10.32604/cmes.2021.011782

Abstract In the present case, we propose the novel generalized fractional integral operator describing Mittag–Leffler function in their kernel with respect to another function Ф. The proposed technique is to use graceful amalgamations of the Riemann–Liouville (RL) fractional integral operator and several other fractional operators. Meanwhile, several generalizations are considered in order to demonstrate the novel variants involving a family of positive functions n (n ∈ N) for the proposed fractional operator. In order to confirm and demonstrate the proficiency of the characterized strategy, we analyze existing fractional integral operators in terms of classical fractional order. Meanwhile, some special cases are… More >

Olumuyiwa J. Peter¹, Amjad S. Shaikh^2,*, Mohammed O. Ibrahim¹, Kottakkaran Sooppy Nisar³, Dumitru Baleanu^4,5,6, Ilyas Khan⁷, Adesoye I. Abioye¹

CMC-Computers, Materials & Continua, Vol.66, No.2, pp. 1823-1848, 2021, DOI:10.32604/cmc.2020.012314

Abstract We propose a mathematical model of the coronavirus disease 2019 (COVID-19) to investigate the transmission and control mechanism of the disease in the community of Nigeria. Using stability theory of differential equations, the qualitative behavior of model is studied. The pandemic indicator represented by basic reproductive number R₀ is obtained from the largest eigenvalue of the next-generation matrix. Local as well as global asymptotic stability conditions for the disease-free and pandemic equilibrium are obtained which determines the conditions to stabilize the exponential spread of the disease. Further, we examined this model by using Atangana–Baleanu fractional derivative operator and existence criteria… More >

Berat Karaagac^{1, 2}, Kolade Matthew Owolabi^{1, 3, *}, Kottakkaran Sooppy Nisar⁴

CMC-Computers, Materials & Continua, Vol.65, No.3, pp. 1905-1924, 2020, DOI:10.32604/cmc.2020.011623

Abstract Illicit drug use is a significant problem that causes great material and moral losses and threatens the future of the society. For this reason, illicit drug use and related crimes are the most significant criminal cases examined by scientists. This paper aims at modeling the illegal drug use using the Atangana-Baleanu fractional derivative with Mittag-Leffler kernel. Also, in this work, the existence and uniqueness of solutions of the fractional-order Illicit drug use model are discussed via Picard-Lindelöf theorem which provides successive approximations using a convergent sequence. Then the stability analysis for both disease-free and endemic equilibrium states is conducted. A… More >