Manal Ghannam¹, Bilgen Kaymakamzade^1,2, Muhammad Farman^1,3,4, Kottakkaran Sooppy Nisar^5,*, Mohammed Altaf Ahmed⁶

CMES-Computer Modeling in Engineering & Sciences, Vol.148, No.1, 2026, DOI:10.32604/cmes.2026.081075 - 27 July 2026

Abstract In Vitro Fertilization (IVF) has been a major medical advancement in the field of fertility treatment. It has helped millions of individuals and couples overcome infertility by providing a workable option. It involves removing eggs from the ovaries of a female, fertilizing those eggs with male sperm in a monitored lab condition. In this work, we developed a new model to show the success of In Vitro Fertilization rates in women through a fractional-order compartmental modeling framework by using real data. The developed model is analyzed statistically, and the biological feasibility of the model. The Lipschitz condition,… More >

Kottakkaran Sooppy Nisar^1,*, Muhammad Farman^2,3,4, Ali Hasan³, Mohammed Altaf Ahmed⁵, Mohammad Tabish⁶

CMES-Computer Modeling in Engineering & Sciences, Vol.147, No.3, 2026, DOI:10.32604/cmes.2026.080973 - 30 June 2026

Abstract A global health concern, neurodegenerative disorders like Parkinson’s and Alzheimer’s impact both mental and physical functioning. The complex interplay among immunological response, protein accumulation, and brain health necessitates sophisticated mathematical modeling. This study introduces a fractional-order mathematical model using the Mittag-Leffler derivative to describe the dynamics of neurodegeneration, incorporating key biological factors such as functioning and infected neurons, extracellular alpha-synuclein, microglia, and T-cells. A fundamental assumption of the model is that neuronal deterioration is influenced by memory effects, where past states impact current disease progression, making fractional-order calculus more suitable than traditional integer-order models. The… More >

Hooi Hung Tang, Te Meng Ting, Nur Syazreen Ahmad^*

CMES-Computer Modeling in Engineering & Sciences, Vol.147, No.3, 2026, DOI:10.32604/cmes.2026.080428 - 30 June 2026

Abstract In industrial and service robotics, autonomous mobile robots must achieve accurate trajectory tracking while maintaining low energy consumption to avoid frequent recharging and performance degradation. Energy efficiency is particularly critical because locomotion accounts for 45%–65% of total power consumption, directly limiting operational range and autonomy. This paper proposes an energy-aware trajectory tracking framework that optimizes a fractional-order proportional-integral-derivative (FOPID) controller using an Enhanced Whale Optimization Algorithm (E-WOA). The key contributions are threefold: (1) the E-WOA hybridizes Differential Evolution (DE)’s global exploration with WOA’s local exploitation to overcome premature convergence in high-dimensional FOPID parameter spaces; (2)… More >

Roshana Mukhtar¹, Chuan-Yu Chang², Muhammad Asif Zahoor Raja^1,*

CMES-Computer Modeling in Engineering & Sciences, Vol.147, No.2, 2026, DOI:10.32604/cmes.2026.079390 - 27 May 2026

Abstract Parkinson’s disease (PD) is a complex neurodegenerative disease associated with the accumulation of α-synuclein, which is linked to the dysfunctional ubiquitin–proteasome system. Fractional calculus has emerged as a powerful tool for modeling complex disease dynamics due to its promising features that inherently capture memory and hereditary effects. This paper presents a fractional-order Proteasome-Fibril interaction model (F-PFIM) for the dynamics of PD, represented by three fractional differential classes, showing concentrations of fibrils (F), proteasomes (P), and proteasome fibril complex (C). The three classes of the F-PFIM collectively make a controlling system that works for the clearance… More > Graphic Abstract

Rajagopalan Ramaswamy^1,*, Gunaseelan Mani², Deepak Kumar³, Ozgur Ege^4,*

CMES-Computer Modeling in Engineering & Sciences, Vol.143, No.2, pp. 1843-1894, 2025, DOI:10.32604/cmes.2025.063672 - 30 May 2025

Abstract The Department of Economic and Social Affairs of the United Nations has released seventeen goals for sustainable development and SDG No. 3 is “Good Health and Well-being”, which mainly emphasizes the strategies to be adopted for maintaining a healthy life. The Monkeypox Virus disease was first reported in 1970. Since then, various health initiatives have been taken, including by the WHO. In the present work, we attempt a fractional model of Monkeypox virus disease, which we feel is crucial for a better understanding of this disease. We use the recently introduced fractional derivative to closely… More >

Aijia Ding, Tingzhang Liu^*

Energy Engineering, Vol.121, No.12, pp. 3735-3759, 2024, DOI:10.32604/ee.2024.054687 - 22 November 2024

Abstract The primary factor contributing to frequency instability in microgrids is the inherent intermittency of renewable energy sources. This paper introduces novel dual-backup controllers utilizing advanced fractional order proportional integral derivative (FOPID) controllers to enhance frequency and tie-line power stability in microgrids amid increasing renewable energy integration. To improve load frequency control, the proposed controllers are applied to a two-area interconnected microgrid system incorporating diverse energy sources, such as wind turbines, photovoltaic cells, diesel generators, and various storage technologies. A novel meta-heuristic algorithm is adopted to select the optimal parameters of the proposed controllers. The efficacy… More >

Muhammad Altaf Khan^1,*, Mahmoud H. DarAssi², Irfan Ahmad³, Noha Mohammad Seyam⁴, Ebraheem Alzahrani⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.141, No.2, pp. 1365-1394, 2024, DOI:10.32604/cmes.2024.053681 - 27 September 2024

Abstract A mathematical model is designed to investigate Tuberculosis (TB) disease under the vaccination, treatment, and environmental impact with real cases. First, we introduce the model formulation in non-integer order derivative and then, extend the model into fractional order derivative. The fractional system’s existence, uniqueness, and other relevant properties are shown. Then, we study the stability analysis of the equilibrium points. The disease-free equilibrium (DFE) is locally asymptotically stable (LAS) when . Further, we show the global asymptotical stability (GAS) of the endemic equilibrium (EE) for and for . The existence of bifurcation analysis in the More >

Muhammad Farman^1,2,4, Ali Akgül^3,9,*, Mir Sajjad Hashemi⁵, Liliana Guran^6,7, Amelia Bucur^8,*

CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.2, pp. 1385-1403, 2024, DOI:10.32604/cmes.2023.028803 - 17 November 2023

Abstract New fractional operators, the COVID-19 model has been studied in this paper. By using different numerical techniques and the time fractional parameters, the mechanical characteristics of the fractional order model are identified. The uniqueness and existence have been established. The model’s Ulam-Hyers stability analysis has been found. In order to justify the theoretical results, numerical simulations are carried out for the presented method in the range of fractional order to show the implications of fractional and fractal orders. We applied very effective numerical techniques to obtain the solutions of the model and simulations. Also, we… More >

Kanhua Su, Jian Wei^*, Meng Li, Hao Li, Wenghao Da, Lang Zhang

Sound & Vibration, Vol.57, pp. 97-117, 2023, DOI:10.32604/sv.2023.043734 - 14 December 2023

Abstract During the drilling process, stick-slip vibration of the drill string is mainly caused by the nonlinear friction generated by the contact between the drill bit and the rock. To eliminate the fatigue wear of downhole drilling tools caused by stick-slip vibrations, the Fractional-Order Proportional-Integral-Derivative (FOPID) controller is used to suppress stick-slip vibrations in the drill string. Although the FOPID controller can effectively suppress the drill string stick-slip vibration, its structure is flexible and parameter setting is complicated, so it needs to use the corresponding machine learning algorithm for parameter optimization. Based on the principle of… More > Graphic Abstract

Lakhlifa Sadek¹, Otmane Sadek¹, Hamad Talibi Alaoui², Mohammed S. Abdo³, Kamal Shah^4,5, Thabet Abdeljawad^4,6,*

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.2, pp. 1931-1950, 2023, DOI:10.32604/cmes.2023.025033 - 06 February 2023

Abstract In this work, we present a model that uses the fractional order Caputo derivative for the novel Coronavirus disease 2019 (COVID-19) with different hospitalization strategies for severe and mild cases and incorporate an awareness program. We generalize the SEIR model of the spread of COVID-19 with a private focus on the transmissibility of people who are aware of the disease and follow preventative health measures and people who are ignorant of the disease and do not follow preventive health measures. Moreover, individuals with severe, mild symptoms and asymptomatically infected are also considered. The basic reproduction… More >