Saqib Murtaza¹, Farhad Ali¹, Aamina^{2, 3, *}, Nadeem Ahmad Sheikh¹, Ilyas Khan⁴, Kottakkaran Sooppy Nisar⁵

CMC-Computers, Materials & Continua, Vol.65, No.3, pp. 2033-2047, 2020, DOI:10.32604/cmc.2020.011817

Abstract It is a very difficult task for the researchers to find the exact solutions to mathematical problems that contain non-linear terms in the equation. Therefore, this article aims to investigate the viscous dissipation (VD) effect on the fractional model of Jeffrey fluid over a heated vertical flat plate that suddenly moves in its own plane. Based on the Atangana-Baleanu operator, the fractional model is developed from the fractional constitutive equations. VD is responsible for the non-linear behavior in the problem. Upon taking the Laplace and Fourier sine transforms, exact expressions have been obtained for momentum and energy equations. The influence… More >

Muhammad Saqib¹, Hanifa Hanif^{1, 2}, T. Abdeljawad^{3, 4, 5}, Ilyas Khan^{6, *}, Sharidan Shafie¹, Kottakkaran Sooppy Nisar⁷

CMC-Computers, Materials & Continua, Vol.65, No.3, pp. 1959-1973, 2020, DOI:10.32604/cmc.2020.011339

Abstract The idea of fractional derivatives is applied to several problems of viscoelastic fluid. However, most of these problems (fluid problems), were studied analytically using different integral transform techniques, as most of these problems are linear. The idea of the above fractional derivatives is rarely applied to fluid problems governed by nonlinear partial differential equations. Most importantly, in the nonlinear problems, either the fractional models are developed by artificial replacement of the classical derivatives with fractional derivatives or simple classical problems (without developing the fractional model even using artificial replacement) are solved. These problems were mostly solved for steady-state fluid problems.… 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 >

Dumitru Baleanu^1,2, Behzad Ghanbari³, Jihad H. Asad^4,*, Amin Jajarmi⁵, Hassan Mohammadi Pirouz⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.3, pp. 953-968, 2020, DOI:10.32604/cmes.2020.010236

Abstract In this work, a system of three masses on the vertices of equilateral triangle is investigated. This system is known in the literature as a planar system. We first give a description to the system by constructing its classical Lagrangian. Secondly, the classical Euler-Lagrange equations (i.e., the classical equations of motion) are derived. Thirdly, we fractionalize the classical Lagrangian of the system, and as a result, we obtain the fractional Euler-Lagrange equations. As the final step, we give the numerical simulations of the fractional model, a new model which is based on Caputo fractional derivative. More >

Dolat Khan¹, Gohar Ali¹, Arshad Khan², Ilyas Khan^{3, *}, Yu-Ming Chu^{4, 5}, Kottakkaran Sooppy Nisar⁶

CMC-Computers, Materials & Continua, Vol.65, No.2, pp. 1237-1251, 2020, DOI:10.32604/cmc.2020.011492

Abstract Nowadays some new ideas of fractional derivatives have been used successfully in the present research community to study different types of mathematical models. Amongst them, the significant models of fluids and heat or mass transfer are on priority. Most recently a new idea of fractal-fractional derivative is introduced; however, it is not used for heat transfer in channel flow. In this article, we have studied this new idea of fractal fractional operators with power-law kernel for heat transfer in a fluid flow problem. More exactly, we have considered the free convection heat transfer for a Newtonian fluid. The flow is… More >

Anees Imtiaz¹, Oi-Mean Foong², Aamina Aamina¹, Nabeel Khan¹, Farhad Ali^{3, 4, *}, Ilyas Khan⁵

CMC-Computers, Materials & Continua, Vol.65, No.1, pp. 171-192, 2020, DOI:10.32604/cmc.2020.011397

Abstract Gold metallic nanoparticles are generally used within a lab as a tracer, to uncover on the presence of specific proteins or DNA in a sample, as well as for the recognition of various antibiotics. They are bio companionable and have properties to carry thermal energy to tumor cells by utilizing different clinical approaches. As the cancer cells are very smaller so for the infiltration, the properly sized nanoparticles have been injected in the blood. For this reason, gold nanoparticles are very effective. Keeping in mind the above applications, in the present work a generalized model of blood flow containing gold… More >

Yun Wang¹, Zhen Wang², Lei Zhang^1,*, Minxu Lu¹

Journal of Renewable Materials, Vol.8, No.7, pp. 819-932, 2020, DOI:10.32604/jrm.2020.09395

Abstract The adsorption process of new nicotinic derivatives on Fe (110) surface and diffusion of corrosive particles in inhibition film were studied by quantum chemistry and molecular dynamics simulation, and inhibition mechanism of inhibitor was discussed. The results indicated that the main active sites of three inhibitors are located in N atoms on the five membered ring. The inhibitor YM-1 has the strongest activity of electrophilic reaction, and the adsorption process of inhibitor molecules is polycentric chemisorption. The adsorption energy for inhibitors followed the order of YM-1 > YM-2 > YM-3. The adsorption film YM-1 more effectively impedes the diffusion and… More >

Şuayip Yüzbaşı^{1, *}, Murat Karaçayır¹

CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.3, pp. 941-956, 2020, DOI:10.32604/cmes.2020.08938

Abstract In this study, we present a numerical scheme similar to the Galerkin method in order to obtain numerical solutions of the Bagley Torvik equation of fractional order 3/2. In this approach, the approximate solution is assumed to have the form of a polynomial in the variable t = x^α , where α is a positive real parameter of our choice. The problem is firstly expressed in vectoral form via substituting the matrix counterparts of the terms present in the equation. After taking inner product of this vector with nonnegative integer powers of t up to a selected positive parameter N,… More >

Muhammad Altaf Khan^1,*, Khanadan Khan², Mohammad A. Safi³, Mahmoud H. DarAssi⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.2, pp. 777-795, 2020, DOI:10.32604/cmes.2020.08208

Abstract The present paper investigates the theoretical analysis of the tuberculosis (TB) model in the discrete-time case. The model is parameterized by the TB infection cases in the Pakistani province of Khyber Pakhtunkhwa between 2002 and 2017. The model is parameterized and the basic reproduction number is obtained and it is found R₀ ¼ 1:5853. The stability analysis for the model is presented and it is shown that the discrete-time tuberculosis model is stable at the disease-free equilibrium whenever R₀ < 1 and further we establish the results for the endemic equilibria and prove that the model is globally asymptotically stable… More >

Muhammad Shuaib¹, Muhammad Bilal¹, Muhammad Altaf Khan^{2, *}, Sharaf J. Malebary³

CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.1, pp. 377-400, 2020, DOI:10.32604/cmes.2020.08076

Abstract An unsteady viscous fluid flow with Dufour and Soret effect, which results in heat and mass transfer due to upward and downward motion of flexible rotating disk, has been studied. The upward or downward motion of non rotating disk results in two dimensional flow, while the vertical action and rotation of the disk results in three dimensional flow. By using an appropriate transformation the governing equations are transformed into the system of ordinary differential equations. The system of ordinary differential equations is further converted into first order differential equation by selecting suitable variables. Then, we generalize the model by using… More >