IDEAS home Printed from https://ideas.repec.org/a/wly/jijmms/v2025y2025i1n9204263.html

Mathematical Model of the Waste Plastic Management via ABC Fractional Order Derivative

Author

Listed:
  • Rajagopalan Ramaswamy
  • Gunaseelan Mani
  • Sugapriya Palanisamy
  • Ozgur Ege

Abstract

Plastic waste can be broadly classified as recyclable and nonrecyclable wastes. The United Nations has set 17 goals of which Goal 14 refers to “Life below Water.” If plastic waste is not properly managed, it can pose a health hazard, including reproductive impairment in marine species. Hence, waste plastic management is necessary to achieve the Goal No. 14 of the SDG Goals of the United Nations, 2030. The primary objective of this paper is to analyze a fractional model of plastic waste management using the recently introduced ABC‐type fractional derivative and to closely examine the plastic waste management model. The Picard ‘Lindelof’ approach is used to investigate their existence and uniqueness. In addition, we obtain approximate solutions of the ABC fractional order waste plastic management model using a numerical technique that combines the ABC fractional derivative with the fundamental theorem of fractional calculus and Lagrange polynomial interpolation. Numerical simulations are used to demonstrate the impact of control parameters on specific compartments within the model and its novelty over other models, supplemented by graphical representations. In this work, we have validated our proposed model by substituting the plastic surface index (PSI) for the fractional order h, which lies in (0, 1). A comparison is also made between plastics or polyethylene and polyvinyl chloride, and the effect of PSI has also been analyzed, so that necessary corrective steps can be taken by the competent authority to achieve SDG Goal 14 and other related goals such as 11, 12, 15, and 17.

Suggested Citation

  • Rajagopalan Ramaswamy & Gunaseelan Mani & Sugapriya Palanisamy & Ozgur Ege, 2025. "Mathematical Model of the Waste Plastic Management via ABC Fractional Order Derivative," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jijmms:v:2025:y:2025:i:1:n:9204263
    DOI: 10.1155/ijmm/9204263
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/ijmm/9204263
    Download Restriction: no
    File URL: https://libkey.io/10.1155/ijmm/9204263?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Jolanta Dąbrowska & Marcin Sobota & Małgorzata Świąder & Paweł Borowski & Andrzej Moryl & Radosław Stodolak & Ewa Kucharczak & Zofia Zięba & Jan K. Kazak, 2021. "Marine Waste—Sources, Fate, Risks, Challenges and Research Needs," IJERPH, MDPI, vol. 18(2), pages 1-17, January.
    2. Vargas-De-León, Cruz, 2011. "On the global stability of SIS, SIR and SIRS epidemic models with standard incidence," Chaos, Solitons & Fractals, Elsevier, vol. 44(12), pages 1106-1110.
    3. Mohammad Izadi & Mahmood Parsamanesh & Waleed Adel, 2022. "Numerical and Stability Investigations of the Waste Plastic Management Model in the Ocean System," Mathematics, MDPI, vol. 10(23), pages 1-26, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fulgensia Kamugisha Mbabazi & J. Y. T. Mugisha & Mark Kimathi, 2020. "Global Stability of Pneumococcal Pneumonia with Awareness and Saturated Treatment," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).
    2. Lei Wang & Zhidong Teng & Long Zhang, 2014. "Global Behaviors of a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Gupta, R.P. & Kumar, Arun, 2022. "Endemic bubble and multiple cusps generated by saturated treatment of an SIR model through Hopf and Bogdanov–Takens bifurcations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 1-21.
    4. Talal Daghriri & Michael Proctor & Sarah Matthews, 2022. "Evolution of Select Epidemiological Modeling and the Rise of Population Sentiment Analysis: A Literature Review and COVID-19 Sentiment Illustration," IJERPH, MDPI, vol. 19(6), pages 1-20, March.
    5. Chaoqian Wang & Hamdi Kavak, 2022. "A General Epidemic Model and Its Application to Mask Design Considering Different Preferences towards Masks," Complexity, John Wiley & Sons, vol. 2022(1).
    6. Tongqian Zhang & Xinzhu Meng & Tonghua Zhang, 2014. "SVEIRS: A New Epidemic Disease Model with Time Delays and Impulsive Effects," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    7. Kuniya, Toshikazu & Muroya, Yoshiaki, 2015. "Global stability of a multi-group SIS epidemic model with varying total population size," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 785-798.
    8. Parsamanesh, Mahmood & Erfanian, Majid, 2018. "Global dynamics of an epidemic model with standard incidence rate and vaccination strategy," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 192-199.
    9. Zhao, Zhen-jun & Liu, Yong-mei & Wang, Ke-xi, 2016. "An analysis of rumor propagation based on propagation force," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 263-271.
    10. Wu, Yucui & Zhang, Zhipeng & Song, Limei & Xia, Chengyi, 2024. "Global stability analysis of two strains epidemic model with imperfect vaccination and immunity waning in a complex network," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    11. Juhui Yan & Wanqin Wu & Qing Miao & Xuewen Tan, 2024. "Global Dynamics and Optimal Control of a Fractional-Order SIV Epidemic Model with Nonmonotonic Occurrence Rate," Mathematics, MDPI, vol. 12(17), pages 1-21, September.
    12. Nudee, K. & Chinviriyasit, S. & Chinviriyasit, W., 2019. "The effect of backward bifurcation in controlling measles transmission by vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 400-412.
    13. Yanfang Liang & Wenlong Wang, 2025. "Dynamic Properties and Chaos Control Analysis of Discrete Epidemic Models Affected by Media Coverage," Mathematics, MDPI, vol. 13(17), pages 1-17, September.
    14. Greenhalgh, D. & Liang, Y. & Mao, X., 2016. "Modelling the effect of telegraph noise in the SIRS epidemic model using Markovian switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 684-704.
    15. Hoang, Manh Tuan & Pham, Hoai Thu, 2025. "Global dynamics and numerical simulation of a modified epidemiological model for viral marketing on social networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 228(C), pages 225-244.
    16. Zhe Yin & Yongguang Yu & Zhenzhen Lu, 2020. "Stability Analysis of an Age-Structured SEIRS Model with Time Delay," Mathematics, MDPI, vol. 8(3), pages 1-17, March.
    17. Chenquan Gan & Xiaofan Yang & Wanping Liu & Qingyi Zhu & Xulong Zhang, 2012. "Propagation of Computer Virus under Human Intervention: A Dynamical Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-8, July.
    18. Mohammad Izadi & Mahmood Parsamanesh & Waleed Adel, 2022. "Numerical and Stability Investigations of the Waste Plastic Management Model in the Ocean System," Mathematics, MDPI, vol. 10(23), pages 1-26, December.
    19. Naim, Mouhcine & Lahmidi, Fouad & Namir, Abdelwahed & Kouidere, Abdelfatah, 2021. "Dynamics of an fractional SEIR epidemic model with infectivity in latent period and general nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    20. Kuncowati & Sholihah Qomariyatus & Ciptadi Gatot & Koderi, 2022. "Handling Waste on Ships: A Model Based on Safety and Awareness," LOGI – Scientific Journal on Transport and Logistics, Sciendo, vol. 13(1), pages 222-232, January.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jijmms:v:2025:y:2025:i:1:n:9204263. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/6396 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.