Mohammad Aslefallah¹, Şuayip Yüzbaşi², Saeid Abbasbandy^1,*

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.2, pp. 1687-1706, 2023, DOI:10.32604/cmes.2023.025647 - 06 February 2023

Abstract In this work, the exponential approximation is used for the numerical simulation of a nonlinear SITR model as a system of differential equations that shows the dynamics of the new coronavirus (COVID-19). The SITR mathematical model is divided into four classes using fractal parameters for COVID-19 dynamics, namely, susceptible (S), infected (I), treatment (T), and recovered (R). The main idea of the presented method is based on the matrix representations of the exponential functions and their derivatives using collocation points. To indicate the usefulness of this method, we employ it in some cases. For error More > Graphic Abstract

Ali Raza¹, Dumitru Baleanu^2,3,4, Zafar Ullah Khan⁵, Muhammad Mohsin^6,*, Nauman Ahmed⁷, Muhammad Rafiq⁸, Pervez Anwar⁹

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.1, pp. 257-275, 2023, DOI:10.32604/cmes.2023.023231 - 05 January 2023

Abstract Most developing countries such as Afghanistan, Pakistan, India, Bangladesh, and many more are still fighting against poliovirus. According to the World Health Organization, approximately eighteen million people have been infected with poliovirus in the last two decades. In Asia, still, some countries are suffering from the virus. The stochastic behavior of the poliovirus through the transition probabilities and non-parametric perturbation with fundamental properties are studied. Some basic properties of the deterministic model are studied, equilibria, local stability around the stead states, and reproduction number. Euler Maruyama, stochastic Euler, and stochastic Runge-Kutta study the behavior of More >

Nesreen Althobaiti¹, Ali Raza^2,*, Arooj Nasir^3,4, 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 >

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 - 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

Nawab Hussain^1,*, Saud M. Alsulami¹, Hind Alamri^1,2,*

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 >

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 - 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 >

Dumitru Baleanu^1,2,3, Mehran Namjoo⁴, Ali Mohebbian⁴, Amin Jajarmi^5,*

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 >

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 >

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 - 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 >

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 - 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 >