IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v174y2023ics0960077923007488.html
   My bibliography  Save this article

Existence and uniqueness of blow-up solution to a fully fractional thermostat model

Author

Listed:
  • Saha, Kiran Kumar
  • Sukavanam, N.

Abstract

In this article, we deal with a fully fractional thermostat model in the settings of the Riemann–Liouville fractional derivatives. The equivalences between the fractional differential equations and the corresponding Volterra–Fredholm integral equations are rigorously derived. By choosing an appropriate weighted Banach space of continuous functions, we employ two standard fixed-point theorems, Leray–Schauder alternative and Banach contraction principle, to establish the existence of blow-up solutions — the unbounded mathematical solutions in the operational interval. Furthermore, an implicit numerical scheme based on the right product rectangle rule is presented, which provides the numerical approximation of the obtained solution. Some examples are provided to validate our theoretical findings, along with numerical simulations of the solutions.

Suggested Citation

  • Saha, Kiran Kumar & Sukavanam, N., 2023. "Existence and uniqueness of blow-up solution to a fully fractional thermostat model," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
  • Handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923007488
    DOI: 10.1016/j.chaos.2023.113847
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923007488
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2023.113847?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Yong Liang, David I. Levine, and Zuo-Jun (Max) Shen, 2012. "Thermostats for the Smart Grid: Models, Benchmarks, and Insights," The Energy Journal, International Association for Energy Economics, vol. 0(Number 4).
    2. Georgios D. Kontes & Georgios I. Giannakis & Philip Horn & Simone Steiger & Dimitrios V. Rovas, 2017. "Using Thermostats for Indoor Climate Control in Office Buildings: The Effect on Thermal Comfort," Energies, MDPI, vol. 10(9), pages 1-22, September.
    3. Haq, Abdul & Sukavanam, N., 2020. "Existence and approximate controllability of Riemann-Liouville fractional integrodifferential systems with damping," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. Haq, Abdul & Sukavanam, N., 2022. "Existence and partial approximate controllability of nonlinear Riemann–Liouville fractional systems of higher order," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    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. Malik, Muslim & Vijayakumar, V. & Shukla, Anurag, 2023. "Controllability of discrete-time semilinear Riemann–Liouville-like fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Yin, Yu-Hang & Lü, Xing, 2024. "Multi-parallelized PINNs for the inverse problem study of NLS typed equations in optical fiber communications: Discovery on diverse high-order terms and variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    3. Li, Xuemei & Liu, Xinge & Tang, Meilan, 2021. "Approximate controllability of fractional evolution inclusions with damping," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    4. Piotr Michalak, 2021. "Selected Aspects of Indoor Climate in a Passive Office Building with a Thermally Activated Building System: A Case Study from Poland," Energies, MDPI, vol. 14(4), pages 1-22, February.
    5. Mohan Raja, M. & Vijayakumar, V., 2022. "Existence results for Caputo fractional mixed Volterra-Fredholm-type integrodifferential inclusions of order r ∈ (1,2) with sectorial operators," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    6. Muhammad Saidu Aliero & Muhammad Asif & Imran Ghani & Muhammad Fermi Pasha & Seung Ryul Jeong, 2022. "Systematic Review Analysis on Smart Building: Challenges and Opportunities," Sustainability, MDPI, vol. 14(5), pages 1-28, March.
    7. Jahangir Hossain & Aida. F. A. Kadir & Ainain. N. Hanafi & Hussain Shareef & Tamer Khatib & Kyairul. A. Baharin & Mohamad. F. Sulaima, 2023. "A Review on Optimal Energy Management in Commercial Buildings," Energies, MDPI, vol. 16(4), pages 1-40, February.
    8. Shiljkut, Vladimir M. & Rajakovic, Nikola Lj., 2015. "Demand response capacity estimation in various supply areas," Energy, Elsevier, vol. 92(P3), pages 476-486.
    9. Abdelhakim Mesloub & Aritra Ghosh & Mabrouk Touahmia & Ghazy Abdullah Albaqawy & Emad Noaime & Badr M. Alsolami, 2020. "Performance Analysis of Photovoltaic Integrated Shading Devices (PVSDs) and Semi-Transparent Photovoltaic (STPV) Devices Retrofitted to a Prototype Office Building in a Hot Desert Climate," Sustainability, MDPI, vol. 12(23), pages 1-17, December.
    10. Haq, Abdul, 2022. "Partial-approximate controllability of semi-linear systems involving two Riemann-Liouville fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    11. Rocha, Paula & Kaut, Michal & Siddiqui, Afzal S., 2016. "Energy-efficient building retrofits: An assessment of regulatory proposals under uncertainty," Energy, Elsevier, vol. 101(C), pages 278-287.
    12. Tu, Gengyang & Faure, Corinne & Schleich, Joachim & Guetlein, Marie-Charlotte, 2021. "The heat is off! The role of technology attributes and individual attitudes in the diffusion of Smart thermostats – findings from a multi-country survey," Technological Forecasting and Social Change, Elsevier, vol. 163(C).
    13. Haq, Abdul & Sukavanam, N., 2022. "Existence and partial approximate controllability of nonlinear Riemann–Liouville fractional systems of higher order," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    14. Georgios D. Kontes & Georgios I. Giannakis & Víctor Sánchez & Pablo De Agustin-Camacho & Ander Romero-Amorrortu & Natalia Panagiotidou & Dimitrios V. Rovas & Simone Steiger & Christopher Mutschler & G, 2018. "Simulation-Based Evaluation and Optimization of Control Strategies in Buildings," Energies, MDPI, vol. 11(12), pages 1-23, December.
    15. Fanghella, Valeria & Faure, Corinne & Guetlein, Marie-Charlotte & Schleich, Joachim, 2022. "Discriminatory subsidies for energy-efficient technologies and the role of envy," Resource and Energy Economics, Elsevier, vol. 68(C).
    16. Edson Manyumbu & Viktoria Martin & Justin Ningwei Chiu, 2023. "Prospective PCM–Desiccant Combination with Solar-Assisted Regeneration for the Indoor Comfort Control of an Office in a Warm and Humid Climate—A Numerical Study," Energies, MDPI, vol. 16(14), pages 1-14, July.
    17. Balázs Cakó & Erzsébet Szeréna Zoltán & János Girán & Gabriella Medvegy & Mária Eördöghné Miklós & Árpád Nyers & Anett Tímea Grozdics & Zsolt Kisander & Viktor Bagdán & Ágnes Borsos, 2021. "An Efficient Method to Compute Thermal Parameters of the Comfort Map Using a Decreased Number of Measurements," Energies, MDPI, vol. 14(18), pages 1-14, September.
    18. Ali Bagheri & Véronique Feldheim & Christos S. Ioakimidis, 2018. "On the Evolution and Application of the Thermal Network Method for Energy Assessments in Buildings," Energies, MDPI, vol. 11(4), pages 1-20, April.
    19. Chappin, Emile J.L. & Schleich, Joachim & Guetlein, Marie-Charlotte & Faure, Corinne & Bouwmans, Ivo, 2022. "Linking of a multi-country discrete choice experiment and an agent-based model to simulate the diffusion of smart thermostats," Technological Forecasting and Social Change, Elsevier, vol. 180(C).
    20. Wang, Yong & Li, Lin, 2013. "Time-of-use based electricity demand response for sustainable manufacturing systems," Energy, Elsevier, vol. 63(C), pages 233-244.

    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:eee:chsofr:v:174:y:2023:i:c:s0960077923007488. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.