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Investigation of the Fractional Strongly Singular Thermostat Model via Fixed Point Techniques

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  • Mohammed K. A. Kaabar

    (Faculty of Science, Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur 50603, Malaysia
    Jabalia Camp, United Nations Relief and Works Agency (UNRWA) Palestinian Refugee Camp, Jabalya, Palestine
    Department of Mathematics and Statistics, Washington State University, Pullman, WA 99163, USA
    These authors contributed equally to this work.)

  • Mehdi Shabibi

    (Department of Mathematics, Mehran Branch, Islamic Azad University, Mehran, Iran
    These authors contributed equally to this work.)

  • Jehad Alzabut

    (Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
    Department of Industrial Engineering, OSTİM Technical University, Ankara 06374, Turkey
    These authors contributed equally to this work.)

  • Sina Etemad

    (Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 53751-71379, Iran
    These authors contributed equally to this work.)

  • Weerawat Sudsutad

    (Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
    These authors contributed equally to this work.)

  • Francisco Martínez

    (Department of Applied Mathematics and Statistics, Technological University of Cartagena, 30203 Cartagena, Spain
    These authors contributed equally to this work.)

  • Shahram Rezapour

    (Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 53751-71379, Iran
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 406040, Taiwan
    These authors contributed equally to this work.)

Abstract

Our main purpose in this paper is to prove the existence of solutions for the fractional strongly singular thermostat model under some generalized boundary conditions. In this way, we use some recent nonlinear fixed-point techniques involving α - ψ -contractions and α -admissible maps. Further, we establish the similar results for the hybrid version of the given fractional strongly singular thermostat control model. Some examples are studied to illustrate the consistency of our results.

Suggested Citation

  • Mohammed K. A. Kaabar & Mehdi Shabibi & Jehad Alzabut & Sina Etemad & Weerawat Sudsutad & Francisco Martínez & Shahram Rezapour, 2021. "Investigation of the Fractional Strongly Singular Thermostat Model via Fixed Point Techniques," Mathematics, MDPI, vol. 9(18), pages 1-21, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2298-:d:637949
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    References listed on IDEAS

    as
    1. Yanliang Dong & Muhammad Zeb & Ghulam Farid & Sidra Bibi & Antonio Masiello, 2021. "Hadamard Inequalities for Strongly α,m-Convex Functions via Caputo Fractional Derivatives," Journal of Mathematics, Hindawi, vol. 2021, pages 1-16, January.
    2. Mohammadi, Hakimeh & Kumar, Sunil & Rezapour, Shahram & Etemad, Sina, 2021. "A theoretical study of the Caputo–Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
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