Chein-Shan Liu¹, Chung-Lun Kuo¹, Chih-Wen Chang^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.3, pp. 3189-3208, 2024, DOI:10.32604/cmes.2023.046002

Abstract To solve the Laplacian problems, we adopt a meshless method with the multiquadric radial basis function (MQ-RBF) as a basis whose center is distributed inside a circle with a fictitious radius. A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function. A sample function is interpolated by the MQ-RBF to provide a trial coefficient vector to compute the merit function. We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm. The novel method provides the optimal values of parameters and,… More >

Yaqing Liu^a,*, Jinyu Ma^b

Frontiers in Heat and Mass Transfer, Vol.6, pp. 1-5, 2015, DOI:10.5098/hmt.6.17

Abstract This paper presents an exact solution for the magnetohydrodynamic (MHD) flow of an incompressible generalized Oldroyd-B fluid due to an infinite accelerating plate. The fractional calculus approach is introduced to establish the constitutive relationship of the Oldroyd-B fluid. The solutions in terms of Fox H-function are obtained by using the Laplace transform. When N = 0 the solutions corresponds to the generalized Oldroyd-B fluids, while θ → 0 and λ → 0 describes the Maxwell fluid and the generalized second fluid, as limiting cases of our general results, respectively. More >

Hong Zhang^1,*, Jiaming Zhou¹, Qi Wang¹, Chengxi Zhu¹, Haijian Shao²

CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.2, pp. 1551-1572, 2023, DOI:10.32604/cmes.2023.027035

Abstract Metal flat surface in-line surface defect detection is notoriously difficult due to obstacles such as high surface reflectivity, pseudo-defect interference, and random elastic deformation. This study evaluates the approach for detecting scratches on a metal surface in order to address a problem in the detection process. This paper proposes an improved Gauss-Laplace (LoG) operator combined with a deep learning technique for metal surface scratch identification in order to solve the difficulties that it is challenging to reduce noise and that the edges are unclear when utilizing existing edge detection algorithms. In the process of scratch identification, it is challenging to… More >

K.V. Chandra Sekhar^*

Frontiers in Heat and Mass Transfer, Vol.16, pp. 1-6, 2021, DOI:10.5098/hmt.16.10

Abstract The behavior of unsteady MHD flow of Jeffrey fluid over an inclined porous plate was analyzed in the present article. The governing partial differential equations of the flow phenomena were solved by using powerful mathematical tool Laplace transforms. The variations of velocity, temperature of the flow with respect to dissimilar physical parameters are analyzed through graphs. The parameters of engineering interest are skin friction and Nusselt number. For better understanding of the problem, variations of skin friction and Nusselt number with respect to critical parameters are tabulated. More >

Utpal Jyoti Das^a , Mira Das^b,*

Frontiers in Heat and Mass Transfer, Vol.17, pp. 1-8, 2021, DOI:10.5098/hmt.17.18

Abstract An unsteady mixed convection flow of an electrically conducting, viscous, incompressible fluid over an oscillating vertical surface in a Darcian porous regime in presence of heat generation/absorption and thermal radiation have been studied. The liquid and the surface is moving with constant angular velocity as a rigid body about an axis. The fluid is taken here to be gray, absorbing/emitting radiation but non scattering medium. Here firstorder chemical reaction and a transverse magnetic field have been considered. The presence of Hall current and Soret effect are considered. The governing coupled partial differential equations are solved by using Laplace transform technique… More >

Muhammad Samraiz¹, Muhammad Umer¹, Thabet Abdeljawad^2,3,*, Saima Naheed¹, Gauhar Rahman⁴, Kamal Shah^2,5

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.1, pp. 901-919, 2023, DOI:10.32604/cmes.2023.024029

Abstract In this paper, we establish the new forms of Riemann-type fractional integral and derivative operators. The novel fractional integral operator is proved to be bounded in Lebesgue space and some classical fractional integral and differential operators are obtained as special cases. The properties of new operators like semi-group, inverse and certain others are discussed and its weighted Laplace transform is evaluated. Fractional integro-differential free-electron laser (FEL) and kinetic equations are established. The solutions to these new equations are obtained by using the modified weighted Laplace transform. The Cauchy problem and a growth model are designed as applications along with graphical… More >

Kamran¹, Siraj Ahmad¹, Kamal Shah^2,3,*, Thabet Abdeljawad^2,4,*, Bahaaeldin Abdalla²

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2743-2765, 2023, DOI:10.32604/cmes.2023.023705

Abstract Laplace transform is one of the powerful tools for solving differential equations in engineering and other science subjects. Using the Laplace transform for solving differential equations, however, sometimes leads to solutions in the Laplace domain that are not readily invertible to the real domain by analytical means. Thus, we need numerical inversion methods to convert the obtained solution from Laplace domain to a real domain. In this paper, we propose a numerical scheme based on Laplace transform and numerical inverse Laplace transform for the approximate solution of fractal-fractional differential equations with order . Our proposed numerical scheme is based on… More > Graphic Abstract

Fairouz Tchier¹, Hassan Khan^2,3,*, Shahbaz Khan², Poom Kumam^4,5, Ioannis Dassios⁶

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2137-2153, 2023, DOI:10.32604/cmes.2023.022855

Abstract The nonlinearity in many problems occurs because of the complexity of the given physical phenomena. The present paper investigates the non-linear fractional partial differential equations’ solutions using the Caputo operator with Laplace residual power series method. It is found that the present technique has a direct and simple implementation to solve the targeted problems. The comparison of the obtained solutions has been done with actual solutions to the problems. The fractional-order solutions are presented and considered to be the focal point of this research article. The results of the proposed technique are highly accurate and provide useful information about the… 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 >

Hung-Hsiang Wang¹, Chih-Ping Chen^2,*

Intelligent Automation & Soft Computing, Vol.32, No.1, pp. 237-254, 2022, DOI:10.32604/iasc.2022.020665

Abstract Machine learning can classify the image clarity of low-cost nailfold capillaroscopy (NC) and can be applied to the design verification for other medical devices. The method can be beneficial for systems that require a large number of image datasets. This investigation covers the design, integration, image sharpness estimation, and deconvolution sharpening of the NC. The study applies this device to record two videos and extract 600 photos, including blurry and sharp images. It then uses the Laplace operator method for blur detection of the pictures. Statistics are recorded for each image’s Laplace score and the distribution of clear photos in… More >