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 - 11 August 2021

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 More >

Rashid Jan¹, Hassan Khan^2,3, Poom Kumam^4,5,*, Fairouz Tchier⁶, Rasool Shah², Haifa Bin Jebreen⁶

CMC-Computers, Materials & Continua, Vol.68, No.3, pp. 3185-3201, 2021, DOI:10.32604/cmc.2021.015252 - 06 May 2021

Abstract It is eminent that partial differential equations are extensively meaningful in physics, mathematics and engineering. Natural phenomena are formulated with partial differential equations and are solved analytically or numerically to interrogate the system’s dynamical behavior. In the present research, mathematical modeling is extended and the modeling solutions Helmholtz equations are discussed in the fractional view of derivatives. First, the Helmholtz equations are presented in Caputo’s fractional derivative. Then Natural transformation, along with the decomposition method, is used to attain the series form solutions of the suggested problems. For justification of the proposed technique, it is More >

Hamid A. Jalab^1,*, Rabha W. Ibrahim², Ali M. Hasan³, Faten Khalid Karim⁴, Ala’a R. Al-Shamasneh¹, Dumitru Baleanu^5,6,7

CMC-Computers, Materials & Continua, Vol.68, No.2, pp. 1467-1483, 2021, DOI:10.32604/cmc.2021.016047 - 13 April 2021

Abstract The enhancement of medical images is a challenging research task due to the unforeseeable variation in the quality of the captured images. The captured images may present with low contrast and low visibility, which might influence the accuracy of the diagnosis process. To overcome this problem, this paper presents a new fractional integral entropy (FITE) that estimates the unforeseeable probabilities of image pixels, posing as the main contribution of the paper. The proposed model dynamically enhances the image based on the image contents. The main advantage of FITE lies in its capability to enhance the… More >

Hamid A. Jalab¹, Ala’a R. Al-Shamasneh¹, Hadil Shaiba², Rabha W. Ibrahim^3,4,*, Dumitru Baleanu^5,6,7

CMC-Computers, Materials & Continua, Vol.67, No.2, pp. 2061-2075, 2021, DOI:10.32604/cmc.2021.015170 - 05 February 2021

Abstract Recently, many rapid developments in digital medical imaging have made further contributions to health care systems. The segmentation of regions of interest in medical images plays a vital role in assisting doctors with their medical diagnoses. Many factors like image contrast and quality affect the result of image segmentation. Due to that, image contrast remains a challenging problem for image segmentation. This study presents a new image enhancement model based on fractional Rényi entropy for the segmentation of kidney MRI scans. The proposed work consists of two stages: enhancement by fractional Rényi entropy, and MRI… 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 - 21 August 2020

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 >

Baofeng Li¹

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.3, pp. 187-202, 2013, DOI:10.3970/cmes.2013.093.187

Abstract In this article, the second kind Chebyshev wavelet method is presented for solving a class of multi-order fractional differential equations (FDEs) with variable coefficients. We first construct the second kind Chebyshev wavelet, prove its convergence and then derive the operational matrix of fractional integration of the second kind Chebyshev wavelet. The operational matrix of fractional integration is utilized to reduce the fractional differential equations to a system of algebraic equations. In addition, illustrative examples are presented to demonstrate the efficiency and accuracy of the proposed method. More >

Antti Lehtinen^a, Reijo Karvinen^b,∗

Frontiers in Heat and Mass Transfer, Vol.2, No.4, pp. 1-6, 2011, DOI:10.5098/hmt.v2.4.3004

Abstract Analytical solutions for three different flat plate conjugate heat transfer cases are presented. The cases are as follows:transient heat transfer of a thin plate with uniform heat generation; the Luikov problem in which one plate surface is kept in a constant temperature and the other one is cooled by forced convection ; and a modified Luikov problem with heat generation on one surface and convection on both surfaces of the plate. All the cases are solved for both laminar and turbulent flows with P r ≥ 1. The solutions in the paper are based on More >