Ndolane Sene^1,*, Ameth Ndiaye²

CMES-Computer Modeling in Engineering & Sciences, Vol.145, No.3, pp. 2849-2852, 2025, DOI:10.32604/cmes.2025.075915 - 23 December 2025

Abstract This article has no abstract. More >

Inga Telksniene¹, Tadas Telksnys², Romas Marcinkevičius³, Zenonas Navickas², Raimondas Čiegis¹, Minvydas Ragulskis^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.145, No.2, pp. 2131-2156, 2025, DOI:10.32604/cmes.2025.072938 - 26 November 2025

Abstract Fractional differential equations (FDEs) provide a powerful tool for modeling systems with memory and non-local effects, but understanding their underlying structure remains a significant challenge. While numerous numerical and semi-analytical methods exist to find solutions, new approaches are needed to analyze the intrinsic properties of the FDEs themselves. This paper introduces a novel computational framework for the structural analysis of FDEs involving iterated Caputo derivatives. The methodology is based on a transformation that recasts the original FDE into an equivalent higher-order form, represented as the sum of a closed-form, integer-order component G(y) and a residual… More >

Manal Adil Murad¹, Shayma Adil Murad^2,*, Thabet Abdeljawad^3,4,5,6,*, Aziz Khan³, D. K. Almutairi⁷

CMES-Computer Modeling in Engineering & Sciences, Vol.143, No.3, pp. 3377-3409, 2025, DOI:10.32604/cmes.2025.064245 - 30 June 2025

Abstract Asthma is the most common allergic disorder and represents a significant global public health problem. Strong evidence suggests a link between ascariasis and asthma. This study aims primarily to determine the prevalence of Ascaris lumbricoides infection among various risk factors, to assess blood parameters, levels of immunoglobulin E (IgE) and interleukin-4 (IL-4), and to explore the relationship between ascariasis and asthma in affected individuals. The secondary objective is to examine a fractal-fractional mathematical model that describes the four stages of the life cycle of Ascaris infection, specifically within the framework of the Caputo-Fabrizio derivative. A… More >

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 >

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 >

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 >

Mustafa Turkyilmazoglu^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.133, No.1, pp. 47-65, 2022, DOI:10.32604/cmes.2022.020781 - 18 July 2022

Abstract An effective solution method of fractional ordinary and partial differential equations is proposed in the present paper. The standard Adomian Decomposition Method (ADM) is modified via introducing a functional term involving both a variable and a parameter. A residual approach is then adopted to identify the optimal value of the embedded parameter within the frame of L² norm. Numerical experiments on sample problems of open literature prove that the presented algorithm is quite accurate, more advantageous over the traditional ADM and straightforward to implement for the fractional ordinary and partial differential equations of the recent focus More >

Mahmoud H. Taha¹, Mohamed A. Ramadan^2,*, Dumitru Baleanu^3,4,5, Galal M. Moatimid¹

CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.3, pp. 969-983, 2020, DOI:10.32604/cmes.2020.010942 - 21 August 2020

Abstract The current paper is concerned with a modified Homotopy perturbation technique. This modification allows achieving an exact solution of an initial value problem of the fractional differential equation. The approach is powerful, effective, and promising in analyzing some classes of fractional differential equations for heat conduction problems and other dynamical systems. To crystallize the new approach, some illustrated examples are introduced. More >