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 >

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 >

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 >

Tahir Naseem¹, Fateh Mebarek-Oudina^2,3,*, Hanumesh Vaidya⁴, Nagina Bibi⁵, Katta Ramesh^6,7, Sami Ullah Khan⁸

CMES-Computer Modeling in Engineering & Sciences, Vol.143, No.1, pp. 351-371, 2025, DOI:10.32604/cmes.2025.063196 - 11 April 2025

Abstract Maximizing the efficiency of thermal engineering equipment involves minimizing entropy generation, which arises from irreversible processes. This study examines thermal transport and entropy generation in viscous flow over a radially stretching disk, incorporating the effects of magnetohydrodynamics (MHD), viscous dissipation, Joule heating, and radiation. Similarity transformations are used to obtain dimensionless nonlinear ordinary differential equations (ODEs) from the governing coupled partial differential equations (PDEs). The converted equations are then solved by using the BVP4C solver in MATLAB. To validate the findings, the results are compared with previously published studies under fixed parameter conditions, demonstrating strong… More >

Umar Shafique¹, Ali Raza^2,7,*, Dumitru Baleanu³, Khadija Nasir⁴, Muhammad Naveed⁵, Abu Bakar Siddique¹, Emad Fadhal^6,*

CMES-Computer Modeling in Engineering & Sciences, Vol.143, No.1, pp. 449-476, 2025, DOI:10.32604/cmes.2025.061635 - 11 April 2025

Abstract Streptococcus suis (S. suis) is a major disease impacting pig farming globally. It can also be transferred to humans by eating raw pork. A comprehensive study was recently carried out to determine the indices through multiple geographic regions in China. Methods: The well-posed theorems were employed to conduct a thorough analysis of the model’s feasible features, including positivity, boundedness equilibria, reproduction number, and parameter sensitivity. Stochastic Euler, Runge Kutta, and Euler Maruyama are some of the numerical techniques used to replicate the behavior of the streptococcus suis infection in the pig population. However, the dynamic… More >

Tsung-Han Li^1,*, Chia-Ming Fan¹, Po-Wei Li²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.32, No.1, pp. 1-1, 2024, DOI:10.32604/icces.2024.012120

Abstract The generalized finite difference method (GFDM), which cooperated with the fictitious-nodes technique, is proposed in this study to accurately analyze three-dimensional boundary value problems, governed by high-order partial differential equations. Some physical applications can be mathematically described by boundary value problems governed by high-order partial differential equations, but it is non-trivial to analyze the high-order partial differential equations by adopting conventional mesh-based numerical schemes, such as finite difference method, the finite element method, etc. In this study, the GFDM, a localized meshless method, is proposed to accurately and efficiently solve boundary value problems governed by… More >