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Search Results (122)
  • Open Access

    ARTICLE

    Cherenkov Radiation: A Stochastic Differential Model Driven by Brownian Motions

    Qingqing Li1,2, Zhiwen Duan1,2,*, Dandan Yang1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.1, pp. 155-168, 2023, DOI:10.32604/cmes.2022.019249

    Abstract With the development of molecular imaging, Cherenkov optical imaging technology has been widely concerned. Most studies regard the partial boundary flux as a stochastic variable and reconstruct images based on the steadystate diffusion equation. In this paper, time-variable will be considered and the Cherenkov radiation emission process will be regarded as a stochastic process. Based on the original steady-state diffusion equation, we first propose a stochastic partial differential equation model. The numerical solution to the stochastic partial differential model is carried out by using the finite element method. When the time resolution is high enough, the numerical solution of the… More >

  • Open Access

    ARTICLE

    The Fractional Investigation of Fornberg-Whitham Equation Using an Efficient Technique

    Hassan Khan1,2, Poom Kumam3,4,*, Asif Nawaz1, Qasim Khan1, Shahbaz Khan1

    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.1, pp. 259-273, 2023, DOI:10.32604/cmes.2022.021332

    Abstract In the last few decades, it has become increasingly clear that fractional calculus always plays a very significant role in various branches of applied sciences. For this reason, fractional partial differential equations (FPDEs) are of more importance to model the different physical processes in nature more accurately. Therefore, the analytical or numerical solutions to these problems are taken into serious consideration and several techniques or algorithms have been developed for their solution. In the current work, the idea of fractional calculus has been used, and fractional Fornberg Whitham equation (FFWE) is represented in its fractional view analysis. A well-known method… More >

  • Open Access

    ARTICLE

    On Fuzzy Conformable Double Laplace Transform with Applications to Partial Differential Equations

    Thabet Abdeljawad1,2, Awais Younus3,*, Manar A. Alqudah4, Usama Atta5

    CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.3, pp. 2163-2191, 2023, DOI:10.32604/cmes.2022.020915

    Abstract The Laplace transformation is a very important integral transform, and it is extensively used in solving ordinary differential equations, partial differential equations, and several types of integro-differential equations. Our purpose in this study is to introduce the notion of fuzzy double Laplace transform, fuzzy conformable double Laplace transform (FCDLT). We discuss some basic properties of FCDLT. We obtain the solutions of fuzzy partial differential equations (both one-dimensional and two-dimensional cases) through the double Laplace approach. We demonstrate through numerical examples that our proposed method is very successful and convenient for resolving partial differential equations. More >

  • Open Access

    ARTICLE

    Numerical Solutions of Fractional Variable Order Differential Equations via Using Shifted Legendre Polynomials

    Kamal Shah1,2, Hafsa Naz2, Thabet Abdeljawad1,3,*, Aziz Khan1, Manar A. Alqudah4

    CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.2, pp. 941-955, 2023, DOI:10.32604/cmes.2022.021483

    Abstract In this manuscript, an algorithm for the computation of numerical solutions to some variable order fractional differential equations (FDEs) subject to the boundary and initial conditions is developed. We use shifted Legendre polynomials for the required numerical algorithm to develop some operational matrices. Further, operational matrices are constructed using variable order differentiation and integration. We are finding the operational matrices of variable order differentiation and integration by omitting the discretization of data. With the help of aforesaid matrices, considered FDEs are converted to algebraic equations of Sylvester type. Finally, the algebraic equations we get are solved with the help of… More >

  • Open Access

    ARTICLE

    Exact Solutions and Finite Time Stability of Linear Conformable Fractional Systems with Pure Delay

    Ahmed M. Elshenhab1,2,*, Xingtao Wang1, Fatemah Mofarreh3, Omar Bazighifan4,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.2, pp. 927-940, 2023, DOI:10.32604/cmes.2022.021512

    Abstract We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay. By using new conformable delayed matrix functions and the method of variation, we obtain a representation of their solutions. As an application, we derive a finite time stability result using the representation of solutions and a norm estimation of the conformable delayed matrix functions. The obtained results are new, and they extend and improve some existing ones. Finally, an example is presented to illustrate the validity of our theoretical results. More >

  • Open Access

    ARTICLE

    LaNets: Hybrid Lagrange Neural Networks for Solving Partial Differential Equations

    Ying Li1, Longxiang Xu1, Fangjun Mei1, Shihui Ying2,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.1, pp. 657-672, 2023, DOI:10.32604/cmes.2022.021277

    Abstract We propose new hybrid Lagrange neural networks called LaNets to predict the numerical solutions of partial differential equations. That is, we embed Lagrange interpolation and small sample learning into deep neural network frameworks. Concretely, we first perform Lagrange interpolation in front of the deep feedforward neural network. The Lagrange basis function has a neat structure and a strong expression ability, which is suitable to be a preprocessing tool for pre-fitting and feature extraction. Second, we introduce small sample learning into training, which is beneficial to guide the model to be corrected quickly. Taking advantages of the theoretical support of traditional… More >

  • Open Access

    ARTICLE

    Breakdown Voltage Prediction by Utilizing the Behavior of Natural Ester for Transformer Applications

    P. Samuel Pakianathan*, R. V. Maheswari

    Intelligent Automation & Soft Computing, Vol.35, No.3, pp. 2717-2736, 2023, DOI:10.32604/iasc.2023.029950

    Abstract This research investigates the dielectric performance of Natural Ester (NE) using the Partial Differential Equation (PDE) tool and analyzes dielectric performance using fuzzy logic. NE nowadays is found to replace Mineral Oil (MO) due to its extensive dielectric properties. Here, the heat-tolerant Natural Esters Olive oil (NE1), Sunflower oil (NE2), and Ricebran oil (NE3) are subjected to High Voltage AC (HVAC) under different electrodes configurations. The breakdown voltage and leakage current of NE1, NE2, and NE3 under Point-Point (P-P), Sphere-Sphere (S-S), Plane-Plane (PL-PL), and Rod-Rod (R-R) are measured, and survival probability is presented. The electric field distribution is analyzed using… More >

  • Open Access

    ARTICLE

    An Efficient Computational Method for Differential Equations of Fractional Type

    Mustafa Turkyilmazoglu1,2,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.133, No.1, pp. 47-65, 2022, DOI:10.32604/cmes.2022.020781

    Abstract An effective solution method of fractional ordinary and partial differential equations is proposed in the present paper. The standard Adomian Decomposition Method (ADM) is modified via introducing a functional term involving both a variable and a parameter. A residual approach is then adopted to identify the optimal value of the embedded parameter within the frame of L2 norm. Numerical experiments on sample problems of open literature prove that the presented algorithm is quite accurate, more advantageous over the traditional ADM and straightforward to implement for the fractional ordinary and partial differential equations of the recent focus of mathematical models. Better… More >

  • Open Access

    ARTICLE

    Reducing the Range of Cancer Risk on BI-RADS 4 Subcategories via Mathematical Modelling

    Nezihal Gokbulut1,2, Evren Hincal1,2,*, Hasan Besim3, Bilgen Kaymakamzade1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.133, No.1, pp. 93-109, 2022, DOI:10.32604/cmes.2022.019782

    Abstract Breast Imaging Reporting and Data System, also known as BI-RADS is a universal system used by radiologists and doctors. It constructs a comprehensive language for the diagnosis of breast cancer. BI-RADS 4 category has a wide range of cancer risk since it is divided into 3 categories. Mathematical models play an important role in the diagnosis and treatment of cancer. In this study, data of 42 BI-RADS 4 patients taken from the Center for Breast Health, Near East University Hospital is utilized. Regarding the analysis, a mathematical model is constructed by dividing the population into 4 compartments. Sensitivity analysis is… More >

  • Open Access

    ARTICLE

    Navier Slip and Heat Transfer in a Nanofluid Due to a Stretching/Shrinking Sheet: An Analytical Study

    A. B. Vishalakshi1, U. S. Mahabaleshwar1,*, M. EL. Ganaoui2, R. Bennacer3

    FDMP-Fluid Dynamics & Materials Processing, Vol.18, No.5, pp. 1551-1567, 2022, DOI:10.32604/fdmp.2022.021949

    Abstract This paper is devoted to the analysis of the heat transfer and Navier’s slip effects in a non-Newtonian Jeffrey fluid flowing past a stretching/shrinking sheet. The nanoparticles, namely, Cu and Al2O3 are used with a water-based fluid with Prandtl number 6.272. Velocity slip flow is assumed to occur when the characteristic size of the flow system is small or the flow pressure is very small. By using the similarity transformations, the governing nonlinear PDEs are turned into ordinary differential equations (ODE’s). Analytical results are presented and analyzed for various values of physical parameters: Prandtl number, Radiation parameter, stretching/shrinking parameter and… More >

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