Gamze Yıldırım^1,2, Şuayip Yüzbaşı^3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.141, No.1, pp. 281-310, 2024, DOI:10.32604/cmes.2024.052181 - 20 August 2024

Abstract In this study, a numerical method based on the Pell-Lucas polynomials (PLPs) is developed to solve the fractional order HIV/AIDS epidemic model with a treatment compartment. The HIV/AIDS mathematical model with a treatment compartment is divided into five classes, namely, susceptible patients (S), HIV-positive individuals (I), individuals with full-blown AIDS but not receiving ARV treatment (A), individuals being treated (T), and individuals who have changed their sexual habits sufficiently (R). According to the method, by utilizing the PLPs and the collocation points, we convert the fractional order HIV/AIDS epidemic model with a treatment compartment into… More >

Anas W. Abulfaraj^*

CMC-Computers, Materials & Continua, Vol.79, No.1, pp. 1137-1156, 2024, DOI:10.32604/cmc.2024.047945 - 25 April 2024

Abstract The utilization of visual attention enhances the performance of image classification tasks. Previous attention-based models have demonstrated notable performance, but many of these models exhibit reduced accuracy when confronted with inter-class and intra-class similarities and differences. Neural-Controlled Differential Equations (N-CDE’s) and Neural Ordinary Differential Equations (NODE’s) are extensively utilized within this context. N-CDE’s possesses the capacity to effectively illustrate both inter-class and intra-class similarities and differences with enhanced clarity. To this end, an attentive neural network has been proposed to generate attention maps, which uses two different types of N-CDE’s, one for adopting hidden layers… More >

Saima Rashid^1,2,*, Fahd Jarad^3,4

CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.3, pp. 2289-2327, 2024, DOI:10.32604/cmes.2023.028773 - 11 March 2024

Abstract Because of the features involved with their varied kernels, differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues. In this paper, we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels. In this approach, the overall population was separated into five cohorts. Furthermore, the descriptive behavior of the system was investigated, including prerequisites for the positivity of solutions, invariant domain of the solution, presence and stability of equilibrium points, and sensitivity analysis. We included a stochastic More >

Sergiy Reutskiy¹, Yuhui Zhang^2,*, Jun Lu^3,*, Ciren Pubu⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.2, pp. 1583-1612, 2024, DOI:10.32604/cmes.2023.044878 - 29 January 2024

Abstract This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations (FODEs) which have been widely used in modeling various phenomena in engineering and science. An approximate solution of the system is sought in the form of the finite series over the Müntz polynomials. By using the collocation procedure in the time interval, one gets the linear algebraic system for the coefficient of the expansion which can be easily solved numerically by a standard procedure. This technique also serves as the basis for solving the time-fractional partial differential equations More >

Rania Saadah¹, Mohammed Amleh¹, Ahmad Qazza¹, Shrideh Al-Omari^2,*, Ahmet Ocak Akdemir³

CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.2, pp. 1593-1616, 2024, DOI:10.32604/cmes.2023.029180 - 17 November 2023

Abstract In this study, we aim to investigate certain triple integral transform and its application to a class of partial differential equations. We discuss various properties of the new transform including inversion, linearity, existence, scaling and shifting, etc. Then, we derive several results enfolding partial derivatives and establish a multi-convolution theorem. Further, we apply the aforementioned transform to some classical functions and many types of partial differential equations involving heat equations, wave equations, Laplace equations, and Poisson equations as well. Moreover, we draw some figures to illustrate 3-D contour plots for exact solutions of some selected More >

V.S. Sampath Kumar, N.P. Pai^† , B. Devaki

Frontiers in Heat and Mass Transfer, Vol.20, pp. 1-13, 2023, DOI:10.5098/hmt.20.30

Abstract In the present study, we consider Casson fluid flow between two porous plates with permeability criteria in the presence of heat transfer and magnetic effect. A proper set of similarity transformations simplify the Navier-Stokes equations to non-linear ODEs with boundary conditions. The homotopy perturbation method is an efficient and stable method which is used to get solutions. Further, the results obtained are compared with the solution computed through an effective and efficient finite difference approach. The purpose of this analysis is to study the four different cases arise viz: suction, injection, mixed suction and mixed More >

Rania Saadeh¹, Ahmad Qazza¹, Aliaa Burqan¹, Shrideh Al-Omari^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.3, pp. 3121-3139, 2023, DOI:10.32604/cmes.2023.026313 - 09 March 2023

Abstract This paper aims to investigate a new efficient method for solving time fractional partial differential equations. In this orientation, a reliable formable transform decomposition method has been designed and developed, which is a novel combination of the formable integral transform and the decomposition method. Basically, certain accurate solutions for time-fractional partial differential equations have been presented. The method under concern demands more simple calculations and fewer efforts compared to the existing methods. Besides, the posed formable transform decomposition method has been utilized to yield a series solution for given fractional partial differential equations. Moreover, several More >

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 >