Amr M. S. Mahdy^1,2,*, Mahmoud Higazy^1,3, Mohamed S. Mohamed^1,4

CMC-Computers, Materials & Continua, Vol.67, No.3, pp. 3463-3486, 2021, DOI:10.32604/cmc.2021.015161

Abstract In this article, the reduced differential transform method is introduced to solve the nonlinear fractional model of Tumor-Immune. The fractional derivatives are described in the Caputo sense. The solutions derived using this method are easy and very accurate. The model is given by its signal flow diagram. Moreover, a simulation of the system by the Simulink of MATLAB is given. The disease-free equilibrium and stability of the equilibrium point are calculated. Formulation of a fractional optimal control for the cancer model is calculated. In addition, to control the system, we propose a novel modification of its model. This modification is… More >

Saqib Murtaza¹, Farhad Ali^2,3,*, Nadeem Ahmad Sheikh¹, Ilyas Khan⁴, Kottakkaran Sooppy Nisar⁵

CMC-Computers, Materials & Continua, Vol.67, No.3, pp. 2915-2932, 2021, DOI:10.32604/cmc.2021.013757

Abstract The present article aims to examine the heat and mass distribution in a free convection flow of electrically conducted, generalized Jeffrey nanofluid in a heated rotatory system. The flow analysis is considered in the presence of thermal radiation and the transverse magnetic field of strength B₀. The medium is porous accepting generalized Darcy’s law. The motion of the fluid is due to the cosine oscillations of the plate. Nanofluid has been formed by the uniform dispersing of the Silver nanoparticles in regular engine oil. The problem has been modeled in the form of classical partial differential equations and then generalized… More >

F. S. Bayones¹, S. M. Abo-Dahab^2,*, Ahmed E. Abouelregal³, A. Al-Mullise¹, S. Abdel-Khalek^1,4, E. M. Khalil^1,5

CMC-Computers, Materials & Continua, Vol.67, No.3, pp. 2899-2913, 2021, DOI:10.32604/cmc.2021.012583

Abstract The present paper paper, we estimate the theory of thermoelasticity a thin slim strip under the variable thermal conductivity in the fractional-order form is solved. Thermal stress theory considering the equation of heat conduction based on the time-fractional derivative of Caputo of order α is applied to obtain a solution. We assumed that the strip surface is to be free from traction and impacted by a thermal shock. The transform of Laplace (LT) and numerical inversion techniques of Laplace were considered for solving the governing basic equations. The inverse of the LT was applied in a numerical manner considering the… More >

Nadeem Ahmad Sheikh^1,2, Dennis Ling Chuan Ching¹, Thabet Abdeljawad^3,4,5, Ilyas Khan^6,*, Muhammad Jamil^7,8, Kottakkaran Sooppy Nisar⁹

CMC-Computers, Materials & Continua, Vol.67, No.2, pp. 1385-1398, 2021, DOI:10.32604/cmc.2021.011986

Abstract An emerging definition of the fractal-fractional operator has been used in this study for the modeling of Casson fluid flow. The magnetohydrodynamics flow of Casson fluid has cogent in a channel where the motion of the upper plate generates the flow while the lower plate is at a static position. The proposed model is non-dimensionalized using the Pi-Buckingham theorem to reduce the complexity in solving the model and computation time. The non-dimensional fractal-fractional model with the power-law kernel has been solved through the Laplace transform technique. The Mathcad software has been used for illustration of the influence of various parameters,… More >

Muhammad Saqib¹, Ilyas Khan^2,*, Sharidan Shafie¹, Ahmad Qushairi Mohamad¹, El-Sayed M. Sherif^3,4

CMC-Computers, Materials & Continua, Vol.67, No.1, pp. 1069-1084, 2021, DOI:10.32604/cmc.2021.012000

Abstract In recent times, scientists and engineers have been most attracted to electrically conducted nanofluids due to their numerous applications in various fields of science and engineering. For example, they are used in cancer treatment (hyperthermia), magnetic resonance imaging (MRI), drug-delivery, and magnetic refrigeration (MR). Bearing in mind the significance and importance of electrically conducted nanofluids, this article aims to study an electrically conducted water-based nanofluid containing carbon nanotubes (CNTs). CNTs are of two types, single-wall carbon nanotubes (SWCNTs) and multiple-wall carbon nanotubes (MWCNTs). The CNTs (SWCNTs and MWCNTs) have been dispersed in regular water as base fluid to form water-CNTs… More >

Anees Imitaz¹, Aamina Aamina¹, Farhad Ali^2,3,*, Ilyas Khan⁴, Kottakkaran Sooppy Nisar⁵

CMC-Computers, Materials & Continua, Vol.66, No.3, pp. 2253-2264, 2021, DOI:10.32604/cmc.2021.012470

Abstract The present study is focused on the unsteady two-phase flow of blood in a cylindrical region. Blood is taken as a counter-example of Brinkman type fluid containing magnetic (dust) particles. The oscillating pressure gradient has been considered because for blood flow it is necessary to investigate in the form of a diastolic and systolic pressure. The transverse magnetic field has been applied externally to the cylindrical tube to study its impact on both fluids as well as particles. The system of derived governing equations based on Navier Stoke’s, Maxwell and heat equations has been generalized using the well-known Caputo–Fabrizio (C–F)… More >

Mohamed Abdelsabour Fahmy^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.1, pp. 175-199, 2021, DOI:10.32604/cmes.2021.012218

Abstract The main aim of this paper is to propose a new memory dependent derivative (MDD) theory which called threetemperature nonlinear generalized anisotropic micropolar-thermoelasticity. The system of governing equations of the problems associated with the proposed theory is extremely difficult or impossible to solve analytically due to nonlinearity, MDD diffusion, multi-variable nature, multi-stage processing and anisotropic properties of the considered material. Therefore, we propose a novel boundary element method (BEM) formulation for modeling and simulation of such system. The computational performance of the proposed technique has been investigated. The numerical results illustrate the effects of time delays and kernel functions on… More >

Anis ur Rehman¹, Farhad Ali¹, Aamina Aamina^2,3,*, Anees Imitaz¹, Ilyas Khan⁴, Kottakkaran Sooppy Nisar⁵

CMC-Computers, Materials & Continua, Vol.66, No.2, pp. 1445-1459, 2021, DOI:10.32604/cmc.2020.012457

Abstract It is of high interest to study laminar flow with mass and heat transfer phenomena that occur in a viscoelastic fluid taken over a vertical plate due to its importance in many technological processes and its increased industrial applications. Because of its wide range of applications, this study aims at evaluating the solutions corresponding to Casson fluids’ oscillating flow using fractional-derivatives. As it has a combined mass-heat transfer effect, we considered the fluid flow upon an oscillatory infinite vertical-plate. Furthermore, we used two new fractional approaches of fractional derivatives, named AB (Atangana–Baleanu) and CF (Caputo–Fabrizio), on dimensionless governing equations and… More >

Yuming Chu¹, Naila Rafiq², Mudassir Shams^3,*, Saima Akram⁴, Nazir Ahmad Mir³, Humaira Kalsoom⁵

CMC-Computers, Materials & Continua, Vol.66, No.1, pp. 275-290, 2021, DOI:10.32604/cmc.2020.011907

Abstract In this article, we construct the most powerful family of simultaneous iterative method with global convergence behavior among all the existing methods in literature for finding all roots of non-linear equations. Convergence analysis proved that the order of convergence of the family of derivative free simultaneous iterative method is nine. Our main aim is to check out the most regularly used simultaneous iterative methods for finding all roots of non-linear equations by studying their dynamical planes, numerical experiments and CPU time-methodology. Dynamical planes of iterative methods are drawn by using MATLAB for the comparison of global convergence properties of simultaneous… More >

An Chen^*

CMES-Computer Modeling in Engineering & Sciences, Vol.125, No.1, pp. 173-195, 2020, DOI:10.32604/cmes.2020.011871

Abstract In this paper, we consider the numerical schemes for a timefractional Oldroyd-B fluid model involving the Caputo derivative. We propose two efficient finite element methods by applying the convolution quadrature in time generated by the backward Euler and the second-order backward difference methods. Error estimates in terms of data regularity are established for both the semidiscrete and fully discrete schemes. Numerical examples for two-dimensional problems further confirm the robustness of the schemes with first- and second-order accurate in time. More >