Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Faculty Publications Article Faculty Publications -Articles Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Creator An entity primarily responsible for making the resource Izadi, Mohammad; Veeresha, Pundikala; Adel, Waleed Title A name given to the resource Mathematical and computational analysis of a fractional-order drug abuse model with nonlinear incidence and logistic growth Date A point or period of time associated with an event in the lifecycle of the resource 01-01-2026 Source A related resource from which the described resource is derived Mathematics and Computers in Simulation;Volume;240;pp.451-472 Identifier An unambiguous reference to the resource within a given context <a href="https://doi.org/10.1016/j.matcom.2025.07.032" target="_blank" rel="noreferrer noopener">https://doi.org/10.1016/j.matcom.2025.07.032</a> <br /><br /><a href="https://www.scopus.com/pages/publications/105011865611?origin=resultslist" target="_blank" rel="noreferrer noopener">https://www.scopus.com/pages/publications/105011865611?origin=resultslist</a> Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Izadi M., Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran, Mahani Math Center, Afzalipour Research Institute, Shahid Bahonar University of Kerman, Kerman, 76169-14111, Iran; Veeresha P., Center for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, 560029, India; Adel W., Laboratoire Interdisciplinaire de l'Universite Francaise d'Egypte (UFEID Lab), Universite Francaise d'Egypte, Cairo, 11837, Egypt, Department of Mathematics and Engineering Physics, Faculty of Engineering, Mansoura University, Mansoura, 35516, Egypt Description An account of the resource This paper presents a novel mathematical model for analyzing the dynamics of drug addiction using a fractional-order system based on the LiouvilleCaputo derivative. The proposed model incorporates a nonlinear saturated incidence rate, logistic growth in the addiction compartments, and seven interconnected subpopulations representing different stages of drug use and recovery, including relapse and awareness. We conduct a rigorous mathematical analysis to establish the existence, uniqueness, positivity, and boundedness of solutions, ensuring the epidemiological and physical validity of the model. The basic reproduction number R0 is derived, and the local and global stability of the equilibrium points is analyzed. A major contribution of this work is the application of a new domain decomposition spectral method based on second-kind Dickson polynomials, combined with the quasilinearization technique, to efficiently solve the complex nonlinear system. The convergence of the numerical method is theoretically validated. Numerical simulations are provided to illustrate the model's dynamics and to explore the impact of various parameters and intervention strategies. Compared to existing models, this study offers an improved framework for understanding memory-dependent behavior in addiction dynamics and introduces a computationally efficient approach to solve fractional-order systems with high accuracy. 2025 International Association for Mathematics and Computers in Simulation (IMACS) Subject The topic of the resource Collocation points; Convergent analysis; Dickson polynomials of the second kind; Drug addicted model; LiouvilleCaputo operator; Stability analysis Publisher An entity responsible for making the resource available Elsevier B.V. Relation A related resource ISSN: 3784754; CODEN: MCSID Language A language of the resource English Type The nature or genre of the resource Article Rights Information about rights held in and over the resource Restricted Access; Hardcopy may be available in the library Format The file format, physical medium, or dimensions of the resource online