Qingqing Li^1,2, Zhiwen Duan^1,2,*, Dandan Yang^1,2

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, More >

Hassan Khan^1,2, Poom Kumam^3,4,*, 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 More >

Thabet Abdeljawad^1,2, Awais Younus^3,*, 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 >

Kamal Shah^1,2, Hafsa Naz², Thabet Abdeljawad^1,3,*, 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 More >

Ahmed M. Elshenhab^1,2,*, Xingtao Wang¹, Fatemah Mofarreh³, Omar Bazighifan^4,*

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 >

Ying Li¹, Longxiang Xu¹, Fangjun Mei¹, Shihui Ying^2,*

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 More >

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… More >

Mustafa Turkyilmazoglu^1,2,*

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 More >

Nezihal Gokbulut^1,2, Evren Hincal^1,2,*, Hasan Besim³, Bilgen Kaymakamzade^1,2

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… More >

A. B. Vishalakshi¹, U. S. Mahabaleshwar^1,*, 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… More >