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 >

Hongwei Ma¹, Yingqian Tian^2,*, Fuzhang Wang^3,*, Quanfu Lou⁴, Lijuan Yu⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.144, No.3, pp. 3419-3432, 2025, DOI:10.32604/cmes.2025.070791 - 30 September 2025

Abstract This study introduces a novel single-layer meshless method, the space-time collocation method based on multiquadric-radial basis functions (MQ-RBF), for solving the Benjamin-Bona-Mahony-Burgers (BBMB) equation. By reconstructing the time variable as a space variable, this method establishes a combined space-time structure that can eliminate the two-step computational process required in traditional grid methods. By introducing shape parameter-optimized MQ-RBF, high-precision discretization of the nonlinear, dispersive, and dissipative terms in the BBMB equation is achieved. The numerical experiment section validates the effectiveness of the proposed method through three benchmark examples. This method shows significant advantages in computational efficiency, More >

Ali Raza^1,*, Asad Ullah², Eugénio M. Rocha¹, Dumitru Baleanu³, Hala H. Taha⁴, Emad Fadhal^5,*

CMES-Computer Modeling in Engineering & Sciences, Vol.144, No.3, pp. 3433-3461, 2025, DOI:10.32604/cmes.2025.069655 - 30 September 2025

Abstract This study investigates the transmission dynamics of conjunctivitis using stochastic delay differential equations (SDDEs). A delayed stochastic model is formulated by dividing the population into five distinct compartments: susceptible, exposed, infected, environmental irritants, and recovered individuals. The model undergoes thorough analytical examination, addressing key dynamical properties including positivity, boundedness, existence, and uniqueness of solutions. Local and global stability around the equilibrium points is studied with respect to the basic reproduction number. The existence of a unique global positive solution for the stochastic delayed model is established. In addition, a stochastic nonstandard finite difference scheme is More >

Junseo Lee¹, Bongsoo Jang¹, Umer Saeed^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.144, No.2, pp. 2165-2189, 2025, DOI:10.32604/cmes.2025.069023 - 31 August 2025

Abstract In recent years, variable-order fractional partial differential equations have attracted growing interest due to their enhanced ability to model complex physical phenomena with memory and spatial heterogeneity. However, existing numerical methods often struggle with the computational challenges posed by such equations, especially in nonlinear, multi-term formulations. This study introduces two hybrid numerical methods—the Linear-Sine and Cosine (L1-CAS) and fast-CAS schemes—for solving linear and nonlinear multi-term Caputo variable-order (CVO) fractional partial differential equations. These methods combine CAS wavelet-based spatial discretization with L1 and fast algorithms in the time domain. A key feature of the approach is More >

Nikolai A. Magnitskii^*

FDMP-Fluid Dynamics & Materials Processing, Vol.21, No.7, pp. 1529-1544, 2025, DOI:10.32604/fdmp.2025.067021 - 31 July 2025

Abstract This paper presents both analytical and numerical studies of the conservative Sawada–Kotera equation and its dissipative generalization, equations known for their soliton solutions and rich chaotic dynamics. These models offer valuable insights into nonlinear wave propagation, with applications in fluid dynamics and materials science, including systems such as liquid crystals and ferrofluids. It is shown that the conservative Sawada–Kotera equation supports traveling wave solutions corresponding to elliptic limit cycles, as well as two- and three-dimensional invariant tori surrounding these cycles in the associated ordinary differential equation (ODE) system. For the dissipative generalized Sawada–Kotera equation, chaotic More >

Tawfeeq Shawly^1,2, Ahmed A. Alsheikhy^3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.143, No.3, pp. 3033-3064, 2025, DOI:10.32604/cmes.2025.065264 - 30 June 2025

Abstract Epilepsy is a long-term neurological condition marked by recurrent seizures, which result from abnormal electrical activity in the brain that disrupts its normal functioning. Traditional methods for detecting epilepsy through machine learning typically utilize discrete-time models, which inadequately represent the continuous dynamics of electroencephalogram (EEG) signals. To overcome this limitation, we introduce an innovative approach that employs Neural Ordinary Differential Equations (NODEs) to model EEG signals as continuous-time systems. This allows for effective management of irregular sampling and intricate temporal patterns. In contrast to conventional techniques, such as Convolutional Neural Networks (CNNs) and Recurrent Neural… 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 >

Ali Raza^1,2,*, Feliz Minhós^2,3,*, Umar Shafique⁴, Muhammad Mohsin⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.143, No.3, pp. 3411-3431, 2025, DOI:10.32604/cmes.2025.060855 - 30 June 2025

Abstract In 2022, Leukemia is the 13th most common diagnosis of cancer globally as per the source of the International Agency for Research on Cancer (IARC). Leukemia is still a threat and challenge for all regions because of 46.6% infection in Asia, and 22.1% and 14.7% infection rates in Europe and North America, respectively. To study the dynamics of Leukemia, the population of cells has been divided into three subpopulations of cells susceptible cells, infected cells, and immune cells. To investigate the memory effects and uncertainty in disease progression, leukemia modeling is developed using stochastic fractional… More >

Seham M. AL-Mekhlafi^1,*, Kamal R. Raslan², Khalid K. Ali², Sadam. H. Alssad^2,3, Nehaya R. Alsenaideh⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.143, No.2, pp. 1927-1953, 2025, DOI:10.32604/cmes.2025.063971 - 30 May 2025

Abstract This study introduces a novel mathematical model to describe the progression of cholera by integrating fractional derivatives with both singular and non-singular kernels alongside stochastic differential equations over four distinct time intervals. The model incorporates three key fractional derivatives: the Caputo-Fabrizio fractional derivative with a non-singular kernel, the Caputo proportional constant fractional derivative with a singular kernel, and the Atangana-Baleanu fractional derivative with a non-singular kernel. We analyze the stability of the core model and apply various numerical methods to approximate the proposed crossover model. To achieve this, the approximation of Caputo proportional constant fractional… More >