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  • Open Access

    ARTICLE

    New Trends in the Modeling of Diseases Through Computational Techniques

    Nesreen Althobaiti1, Ali Raza2,*, Arooj Nasir3,4, Jan Awrejcewicz5, Muhammad Rafiq6, Nauman Ahmed7, Witold Pawłowski8, Muhammad Jawaz7, Emad E. Mahmoud1

    Computer Systems Science and Engineering, Vol.45, No.3, pp. 2935-2951, 2023, DOI:10.32604/csse.2023.033935 - 21 December 2022

    Abstract The computational techniques are a set of novel problem-solving methodologies that have attracted wider attention for their excellent performance. The handling strategies of real-world problems are artificial neural networks (ANN), evolutionary computing (EC), and many more. An estimated fifty thousand to ninety thousand new leishmaniasis cases occur annually, with only 25% to 45% reported to the World Health Organization (WHO). It remains one of the top parasitic diseases with outbreak and mortality potential. In 2020, more than ninety percent of new cases reported to World Health Organization (WHO) occurred in ten countries: Brazil, China, Ethiopia,… More >

  • Open Access

    ARTICLE

    On the Approximation of Fractal-Fractional Differential Equations Using Numerical Inverse Laplace Transform Methods

    Kamran1, Siraj Ahmad1, Kamal Shah2,3,*, Thabet Abdeljawad2,4,*, Bahaaeldin Abdalla2

    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2743-2765, 2023, DOI:10.32604/cmes.2023.023705 - 23 November 2022

    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… More > Graphic Abstract

    On the Approximation of Fractal-Fractional Differential Equations Using Numerical Inverse Laplace Transform Methods

  • Open Access

    ARTICLE

    Solving Fractional Differential Equations via Fixed Points of Chatterjea Maps

    Nawab Hussain1,*, Saud M. Alsulami1, Hind Alamri1,2,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2617-2648, 2023, DOI:10.32604/cmes.2023.023143 - 23 November 2022

    Abstract In this paper, we present the existence and uniqueness of fixed points and common fixed points for Reich and Chatterjea pairs of self-maps in complete metric spaces. Furthermore, we study fixed point theorems for Reich and Chatterjea nonexpansive mappings in a Banach space using the Krasnoselskii-Ishikawa iteration method associated with and consider some applications of our results to prove the existence of solutions for nonlinear integral and nonlinear fractional differential equations. We also establish certain interesting examples to illustrate the usability of our results. More >

  • Open Access

    ARTICLE

    The Fractional Investigation of Some Nonlinear Partial Differential Equations by Using an Efficient Procedure

    Fairouz Tchier1, Hassan Khan2,3,*, Shahbaz Khan2, Poom Kumam4,5, Ioannis Dassios6

    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2137-2153, 2023, DOI:10.32604/cmes.2023.022855 - 23 November 2022

    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 More >

  • Open Access

    ARTICLE

    A Weighted Average Finite Difference Scheme for the Numerical Solution of Stochastic Parabolic Partial Differential Equations

    Dumitru Baleanu1,2,3, Mehran Namjoo4, Ali Mohebbian4, Amin Jajarmi5,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.2, pp. 1147-1163, 2023, DOI:10.32604/cmes.2022.022403 - 27 October 2022

    Abstract In the present paper, the numerical solution of Itô type stochastic parabolic equation with a time white noise process is imparted based on a stochastic finite difference scheme. At the beginning, an implicit stochastic finite difference scheme is presented for this equation. Some mathematical analyses of the scheme are then discussed. Lastly, to ascertain the efficacy and accuracy of the suggested technique, the numerical results are discussed and compared with the exact solution. More >

  • Open Access

    ARTICLE

    Towards a Unified Single Analysis Framework Embedded with Multiple Spatial and Time Discretized Methods for Linear Structural Dynamics

    David Tae, Kumar K. Tamma*

    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.2, pp. 843-885, 2023, DOI:10.32604/cmes.2023.023071 - 27 October 2022

    Abstract We propose a novel computational framework that is capable of employing different time integration algorithms and different space discretized methods such as the Finite Element Method, particle methods, and other spatial methods on a single body sub-divided into multiple subdomains. This is in conjunction with implementing the well known Generalized Single Step Single Solve (GS4) family of algorithms which encompass the entire scope of Linear Multistep algorithms that have been developed over the past 50 years or so and are second order accurate into the Differential Algebraic Equation framework. In the current state of technology,… More >

  • 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 - 29 September 2022

    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 >

  • 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 - 29 September 2022

    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 >

  • 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 - 20 September 2022

    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 - 31 August 2022

    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 >

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