Muath Awadalla^1,*, Kinda Abuasbeh¹, Yves Yannick Yameni Noupoue², Mohammed S. Abdo³

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2767-2785, 2023, DOI:10.32604/cmes.2023.024036

Abstract This study focuses on the dynamics of drug concentration in the blood. In general, the concentration level of a drug in the blood is evaluated by the mean of an ordinary and first-order differential equation. More precisely, it is solved through an initial value problem. We proposed a new modeling technique for studying drug concentration in blood dynamics. This technique is based on two fractional derivatives, namely, Caputo and Caputo-Fabrizio derivatives. We first provided comprehensive and detailed proof of the existence of at least one solution to the problem; we later proved the uniqueness of the existing solution. The proof… More >

Nasir Mahmud Khokhar¹, Muhammad Nadeem Majeed², Syed Muslim Shah^3,*

CMC-Computers, Materials & Continua, Vol.70, No.2, pp. 2209-2224, 2022, DOI:10.32604/cmc.2022.019120

Abstract In this study, it is proposed that the diffusion least mean square (LMS) algorithm can be improved by applying the fractional order signal processing methodologies. Application of Caputo’s fractional derivatives are considered in the optimization of cost function. It is suggested to derive a fractional order variant of the diffusion LMS algorithm. The applicability is tested for the estimation of channel parameters in a distributed environment consisting of randomly distributed sensors communicating through wireless medium. The topology of the network is selected such that a smaller number of nodes are informed. In the network, a random sleep strategy is followed… More >

I. G. Ameen¹, N. A. Elkot², M. A. Zaky^3,*, A. S. Hendy^4,5, E. H. Doha²

CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.1, pp. 21-41, 2021, DOI:10.32604/cmes.2021.015310

Abstract We target here to solve numerically a class of nonlinear fractional two-point boundary value problems involving left- and right-sided fractional derivatives. The main ingredient of the proposed method is to recast the problem into an equivalent system of weakly singular integral equations. Then, a Legendre-based spectral collocation method is developed for solving the transformed system. Therefore, we can make good use of the advantages of the Gauss quadrature rule. We present the construction and analysis of the collocation method. These results can be indirectly applied to solve fractional optimal control problems by considering the corresponding Euler–Lagrange equations. Two numerical examples… 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 >

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 >

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 >

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 >

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 >

Yanxin Wang^{1, *}, Li Zhu¹, Zhi Wang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.118, No.2, pp. 339-350, 2019, DOI:10.31614/cmes.2019.04575

Abstract An Euler wavelets method is proposed to solve a class of nonlinear variable order fractional differential equations in this paper. The properties of Euler wavelets and their operational matrix together with a family of piecewise functions are first presented. Then they are utilized to reduce the problem to the solution of a nonlinear system of algebraic equations. And the convergence of the Euler wavelets basis is given. The method is computationally attractive and some numerical examples are provided to illustrate its high accuracy. More >

H. S. Shukla¹, Mohammad Tamsir¹, Vineet K. Srivastava², Jai Kumar³

CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.1, pp. 1-17, 2014, DOI:10.3970/cmes.2014.103.001

Abstract The objective of this article is to carry out an approximate analytical solution of the time fractional order Cauchy-reaction diffusion equation by using a semi analytical method referred as the fractional-order reduced differential transform method (FRDTM). The fractional derivative is illustrated in the Caputo sense. The FRDTM is very efficient and effective powerful mathematical tool for solving wide range of real world physical problems by providing an exact or a closed approximate solution of any differential equation arising in engineering and allied sciences. Four test numerical examples are provided to validate and illustrate the efficiency of FRDTM. More >