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  • Open Access

    ARTICLE

    Predictive and Global Effect of Active Smoker in Asthma Dynamics with Caputo Fractional Derivative

    Muhammad Farman1,2,3,*, Noreen Asghar4, Muhammad Umer Saleem4, Kottakkaran Sooppy Nisar5,6, Kamyar Hosseini1,2,7, Mohamed Hafez8,9

    CMES-Computer Modeling in Engineering & Sciences, Vol.145, No.1, pp. 721-751, 2025, DOI:10.32604/cmes.2025.069541 - 30 October 2025

    Abstract Smoking is harmful to the lungs and has numerous effects on our bodies. This leads to decreased lung function, which increases the lungs’ susceptibility to asthma triggers. In this paper, we develop a new fractional-order model and investigate the impact of smoking on the progression of asthma by using the Caputo operator to analyze different factors. Using the Banach contraction principle, the existence and uniqueness of solutions are established, and the positivity and boundedness of the model are proved. The model further incorporates different stages of smoking to account for incubation periods and other latent… More >

  • Open Access

    ARTICLE

    Analysis of a Laplace Spectral Method for Time-Fractional Advection-Diffusion Equations Incorporating the Atangana-Baleanu Derivative

    Kamran1,*, Farman Ali Shah1, Kallekh Afef 2, J. F. Gómez-Aguilar 3, Salma Aljawi4, Ioan-Lucian Popa5,6,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.143, No.3, pp. 3433-3462, 2025, DOI:10.32604/cmes.2025.064815 - 30 June 2025

    Abstract In this article, we develop the Laplace transform (LT) based Chebyshev spectral collocation method (CSCM) to approximate the time fractional advection-diffusion equation, incorporating the Atangana-Baleanu Caputo (ABC) derivative. The advection-diffusion equation, which governs the transport of mass, heat, or energy through combined advection and diffusion processes, is central to modeling physical systems with nonlocal behavior. Our numerical scheme employs the LT to transform the time-dependent time-fractional PDEs into a time-independent PDE in LT domain, eliminating the need for classical time-stepping methods that often suffer from stability constraints. For spatial discretization, we employ the CSCM, where More >

  • Open Access

    ARTICLE

    Epidemiological Modeling of Pneumococcal Pneumonia: Insights from ABC Fractal-Fractional Derivatives

    Mohammed Althubyani1,*, Nidal E. Taha2, Khdija O. Taha2, Rasmiyah A. Alharb2, Sayed Saber1,3

    CMES-Computer Modeling in Engineering & Sciences, Vol.143, No.3, pp. 3491-3521, 2025, DOI:10.32604/cmes.2025.061640 - 30 June 2025

    Abstract This study investigates the dynamics of pneumococcal pneumonia using a novel fractal-fractional Susceptible-Carrier-Infected-Recovered model formulated with the Atangana-Baleanu in Caputo (ABC) sense. Unlike traditional epidemiological models that rely on classical or Caputo fractional derivatives, the proposed model incorporates nonlocal memory effects, hereditary properties, and complex transmission dynamics through fractal-fractional calculus. The Atangana-Baleanu operator, with its non-singular Mittag-Leffler kernel, ensures a more realistic representation of disease progression compared to classical integer-order models and singular kernel-based fractional models. The study establishes the existence and uniqueness of the proposed system and conducts a comprehensive stability analysis, including local More >

  • Open Access

    ARTICLE

    Numerical Treatments for a Crossover Cholera Mathematical Model Combining Different Fractional Derivatives Based on Nonsingular and Singular Kernels

    Seham M. AL-Mekhlafi1,*, Kamal R. Raslan2, Khalid K. Ali2, Sadam. H. Alssad2,3, 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 >

  • Open Access

    ARTICLE

    An Efficient Technique for One-Dimensional Fractional Diffusion Equation Model for Cancer Tumor

    Daasara Keshavamurthy Archana1, Doddabhadrappla Gowda Prakasha1, Pundikala Veeresha2, Kottakkaran Sooppy Nisar3,4,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.141, No.2, pp. 1347-1363, 2024, DOI:10.32604/cmes.2024.053916 - 27 September 2024

    Abstract This study intends to examine the analytical solutions to the resulting one-dimensional differential equation of a cancer tumor model in the frame of time-fractional order with the Caputo-fractional operator employing a highly efficient methodology called the -homotopy analysis transform method. So, the preferred approach effectively found the analytic series solution of the proposed model. The procured outcomes of the present framework demonstrated that this method is authentic for obtaining solutions to a time-fractional-order cancer model. The results achieved graphically specify that the concerned paradigm is dependent on arbitrary order and parameters and also disclose the More >

  • Open Access

    ARTICLE

    Numerical Treatments for Crossover Cancer Model of Hybrid Variable-Order Fractional Derivatives

    Nasser Sweilam1, Seham Al-Mekhlafi2,*, Aya Ahmed3, Ahoud Alsheri4, Emad Abo-Eldahab3

    CMES-Computer Modeling in Engineering & Sciences, Vol.140, No.2, pp. 1619-1645, 2024, DOI:10.32604/cmes.2024.047896 - 20 May 2024

    Abstract In this paper, two crossover hybrid variable-order derivatives of the cancer model are developed. Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators. The existence, uniqueness, and stability of the proposed model are discussed. Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models. Comparative studies with generalized fifth-order Runge-Kutta method are given. Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented. We have showcased the efficiency of the proposed More >

  • Open Access

    ARTICLE

    A New Scheme of the ARA Transform for Solving Fractional-Order Waves-Like Equations Involving Variable Coefficients

    Yu-Ming Chu1, Sobia Sultana2, Shazia Karim3, Saima Rashid4,*, Mohammed Shaaf Alharthi5

    CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.1, pp. 761-791, 2024, DOI:10.32604/cmes.2023.028600 - 22 September 2023

    Abstract The goal of this research is to develop a new, simplified analytical method known as the ARA-residue power series method for obtaining exact-approximate solutions employing Caputo type fractional partial differential equations (PDEs) with variable coefficient. ARA-transform is a robust and highly flexible generalization that unifies several existing transforms. The key concept behind this method is to create approximate series outcomes by implementing the ARA-transform and Taylor’s expansion. The process of finding approximations for dynamical fractional-order PDEs is challenging, but the ARA-residual power series technique magnifies this challenge by articulating the solution in a series pattern… More >

  • Open Access

    ARTICLE

    New Configurations of the Fuzzy Fractional Differential Boussinesq Model with Application in Ocean Engineering and Their Analysis in Statistical Theory

    Yu-Ming Chu1, Saima Rashid2,*, 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 >

  • Open Access

    ARTICLE

    MHD FLOW OF JEFFREY FLUID WITH HEAT ABSORPTION AND THERMO-DIFFUSION

    Ahmad Shafiquea , Muhammad Ramzana,*, Zubda Ikrama, M. Amira, Mudassar Nazara

    Frontiers in Heat and Mass Transfer, Vol.20, pp. 1-10, 2023, DOI:10.5098/hmt.20.4

    Abstract Unsteady flow of fractionalized Jeffrey fluid over a plate is considered. In addition, thermo diffusion and slip effects are also used in the problem. The flow model is solved using Constant proportional Caputo fractional derivative. Initially, the governing equations are made non-dimensional and then solved by Laplace transform. From the Figs., it is observed that Prandtl and Smith numbers have decreasing effect on fluid motion, whereas thermodiffusion have increasing effect on fluid motion. Moreover, comparison among fractionalized and ordinary velocity fields is also drawn. More >

  • Open Access

    ARTICLE

    A Study on the Nonlinear Caputo-Type Snakebite Envenoming Model with Memory

    Pushpendra Kumar1,*, Vedat Suat Erturk2, V. Govindaraj1, Dumitru Baleanu3,4,5

    CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.3, pp. 2487-2506, 2023, DOI:10.32604/cmes.2023.026009 - 09 March 2023

    Abstract In this article, we introduce a nonlinear Caputo-type snakebite envenoming model with memory. The well-known Caputo fractional derivative is used to generalize the previously presented integer-order model into a fractional-order sense. The numerical solution of the model is derived from a novel implementation of a finite-difference predictor-corrector (L1-PC) scheme with error estimation and stability analysis. The proof of the existence and positivity of the solution is given by using the fixed point theory. From the necessary simulations, we justify that the first-time implementation of the proposed method on an epidemic model shows that the scheme More >

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