Yaya Wang¹, P. Veeresha², D. G. Prakasha³, Haci Mehmet Baskonus^4,*, Wei Gao⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.133, No.3, pp. 697-717, 2022, DOI:10.32604/cmes.2022.021865

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,… More >

Ritam Sharma¹, Janki Ballabh Sharma¹, Ranjan Maheshwari¹, Praveen Agarwal^2,3,4,5,*

CMES-Computer Modeling in Engineering & Sciences, Vol.130, No.2, pp. 923-947, 2022, DOI:10.32604/cmes.2022.016065

Abstract In this paper, a novel hybrid texture feature set and fractional derivative filter-based breast cancer detection model is introduced. This paper also introduces the application of a histogram of linear bipolar pattern features (HLBP) for breast thermogram classification. Initially, breast tissues are separated by masking operation and filtered by Grmwald–Letnikov fractional derivative-based Sobel mask to enhance the texture and rectify the noise. A novel hybrid feature set using HLBP and other statistical feature sets is derived and reduced by principal component analysis. Radial basis function kernel-based support vector machine is employed for detecting the abnormality in the thermogram. The performance… 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 >

Ravi Shanker Dubey¹, Dumitru Baleanu^2,3, Manvendra Narayan Mishra^1,*, Pranay Goswami⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.3, pp. 1247-1263, 2021, DOI:10.32604/cmes.2021.015224

Abstract Diabetes is a burning issue in the whole world. It is the imbalance between body glucose and insulin. The study of this imbalance is very much needed from a research point of view. For this reason, Bergman gave an important model named-Bergman minimal model. In the present work, using Caputo-Fabrizio (CF) fractional derivative, we generalize Bergman’s minimal blood glucose-insulin model. Further, we modify the old model by including one more component known as diet D(t), which is also essential for the blood glucose model. We solve the modified model with the help of Sumudu transform and fixed-point iteration procedures. Also,… 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 >

Muhammad Amin¹, Muhammad Abbas^2,*, Dumitru Baleanu^3,4,5, Muhammad Kashif Iqbal⁶, Muhammad Bilal Riaz⁷

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.1, pp. 361-384, 2021, DOI:10.32604/cmes.2021.012720

Abstract This work is concerned with the application of a redefined set of extended uniform cubic B-spline (RECBS) functions for the numerical treatment of time-fractional Telegraph equation. The presented technique engages finite difference formulation for discretizing the Caputo time-fractional derivatives and RECBS functions to interpolate the solution curve along the spatial grid. Stability analysis of the scheme is provided to ensure that the errors do not amplify during the execution of the numerical procedure. The derivation of uniform convergence has also been presented. Some computational experiments are executed to verify the theoretical considerations. Numerical results are compared with the existing schemes… 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 >