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 >

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 >

Yu-Ming Chu¹, Sobia Sultana², Saima Rashid^3,*, Mohammed Shaaf Alharthi⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.3, pp. 2427-2464, 2023, DOI:10.32604/cmes.2023.028771 - 03 August 2023

Abstract Various data sets showing the prevalence of numerous viral diseases have demonstrated that the transmission is not truly homogeneous. Two examples are the spread of Spanish flu and COVID-19. The aim of this research is to develop a comprehensive nonlinear stochastic model having six cohorts relying on ordinary differential equations via piecewise fractional differential operators. Firstly, the strength number of the deterministic case is carried out. Then, for the stochastic model, we show that there is a critical number that can predict virus persistence and infection eradication. Because of the peculiarity of More >

Maha Noorwali¹, Mohammed Shehu Shagari^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.2, pp. 1937-1956, 2023, DOI:10.32604/cmes.2023.028239 - 26 June 2023

Abstract The real world is filled with uncertainty, vagueness, and imprecision. The concepts we meet in everyday life are vague rather than precise. In real-world situations, if a model requires that conclusions drawn from it have some bearings on reality, then two major problems immediately arise, viz. real situations are not usually crisp and deterministic; complete descriptions of real systems often require more comprehensive data than human beings could recognize simultaneously, process and understand. Conventional mathematical tools which require all inferences to be exact, are not always efficient to handle imprecisions in a wide variety of… More >

Yu-Ming Chu¹, Saima Rashid^2,*, Shazia Karim³, Anam Sultan²

CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.2, pp. 1573-1611, 2023, DOI:10.32604/cmes.2023.027724 - 26 June 2023

Abstract The fractional-order Boussinesq equations (FBSQe) are investigated in this work to see if they can effectively improve the situation where the shallow water equation cannot directly handle the dispersion wave. The fuzzy forms of analytical FBSQe solutions are first derived using the Adomian decomposition method. It also occurs on the sea floor as opposed to at the functionality. A set of dynamical partial differential equations (PDEs) in this article exemplify an unconfined aquifer flow implication. This methodology can accurately simulate climatological intrinsic waves, so the ripples are spread across a large demographic zone. The Aboodh… 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 >

Kamal Shah^1,2, Thabet Abdeljawad^3,4,*, Fahd Jarad⁵, Qasem Al-Mdallal⁶

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.2, pp. 1457-1472, 2023, DOI:10.32604/cmes.2023.021523 - 06 February 2023

Abstract This article studies a nonlinear fractional order Lotka-Volterra prey-predator type dynamical system. For the proposed study, we consider the model under the conformable fractional order derivative (CFOD). We investigate the mentioned dynamical system for the existence and uniqueness of at least one solution. Indeed, Schauder and Banach fixed point theorems are utilized to prove our claim. Further, an algorithm for the approximate analytical solution to the proposed problem has been established. In this regard, the conformable fractional differential transform (CFDT) technique is used to compute the required results in the form of a series. Using 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 >

Ayesha Heena^1,*, Nagashettappa Biradar¹, Najmuddin M. Maroof², Surbhi Bhatia³, Arwa Mashat⁴, Shakila Basheer⁵

Computer Systems Science and Engineering, Vol.45, No.2, pp. 1409-1422, 2023, DOI:10.32604/csse.2023.029611 - 03 November 2022

Abstract Image enhancement is an important preprocessing task as the contrast is low in most of the medical images, Therefore, enhancement becomes the mandatory process before actual image processing should start. This research article proposes an enhancement of the model-based differential operator for the images in general and Echocardiographic images, the proposed operators are based on Grunwald-Letnikov (G-L), Riemann-Liouville (R-L) and Caputo (Li & Xie), which are the definitions of fractional order calculus. In this fractional-order, differentiation is well focused on the enhancement of echocardiographic images. This provoked for developing a non-linear filter mask for image… More >