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  • Open Access


    On Parametric Fuzzy Linear Programming Formulated by a Fractal

    Rafid A. Al-Saeedi1, Rabha W. Ibrahim2, Rafida M. Elobaid3,*

    Intelligent Automation & Soft Computing, Vol.30, No.3, pp. 1073-1084, 2021, DOI:10.32604/iasc.2021.018011

    Abstract Fractal strategy is an important tool in manufacturing proposals, including computer design, conserving, power supplies and decorations. In this work, a parametric programming, analysis is proposed to mitigate an optimization problem. By employing a fractal difference equation of the spread functions (local fractional calculus operator) in linear programming, we aim to analyze the restraints and the objective function. This work proposes a new technique of fractal fuzzy linear programming (FFLP) model based on the symmetric triangular fuzzy number. The parameter fuzzy number is selected from the fractal power of the difference equation. Note that this… More >

  • Open Access


    Solution of Modified Bergman Minimal Blood Glucose-Insulin Model Using Caputo-Fabrizio Fractional Derivative

    Ravi Shanker Dubey1, Dumitru Baleanu2,3, Manvendra Narayan Mishra1,*, 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 More >

  • Open Access


    The Investigation of the Fractional-View Dynamics of Helmholtz Equations Within Caputo Operator

    Rashid Jan1, Hassan Khan2,3, Poom Kumam4,5,*, 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

    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 >

  • Open Access


    A New Medical Image Enhancement Algorithm Based on Fractional Calculus

    Hamid A. Jalab1,*, Rabha W. Ibrahim2, Ali M. Hasan3, Faten Khalid Karim4, Ala’a R. Al-Shamasneh1, Dumitru Baleanu5,6,7

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

    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 >

  • Open Access


    Fractional Rényi Entropy Image Enhancement for Deep Segmentation of Kidney MRI

    Hamid A. Jalab1, Ala’a R. Al-Shamasneh1, Hadil Shaiba2, Rabha W. Ibrahim3,4,*, Dumitru Baleanu5,6,7

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

    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 >

  • Open Access


    Planar System-Masses in an Equilateral Triangle: Numerical Study within Fractional Calculus

    Dumitru Baleanu1,2, Behzad Ghanbari3, Jihad H. Asad4,*, 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 >

  • Open Access


    The Second Kind Chebyshev Wavelet Method for Fractional Differential Equations with Variable Coefficients

    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 >

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