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On a Lyapunov-Type Inequality for Control of a ψ -Model Thermostat and the Existence of Its Solutions

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  • Shahram Rezapour

    (Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan)

  • Sina Etemad

    (Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran)

  • Ravi P. Agarwal

    (Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363, USA)

  • Kamsing Nonlaopon

    (Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand)

Abstract

In this paper, a new structure of an applied model of thermostat is defined using the generalized ψ -operators with three-point boundary conditions. Some useful properties of the relevant Green’s function are established, and based on these properties, the Lyapunov-type inequality is constructed for the given extended ψ -model thermostat with the help of Jensen’s inequality. By defining mild solutions for such an extended system, the existence and non-existence conditions are discussed.

Suggested Citation

  • Shahram Rezapour & Sina Etemad & Ravi P. Agarwal & Kamsing Nonlaopon, 2022. "On a Lyapunov-Type Inequality for Control of a ψ -Model Thermostat and the Existence of Its Solutions," Mathematics, MDPI, vol. 10(21), pages 1-11, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4023-:d:957845
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    References listed on IDEAS

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    1. 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).
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    3. Etemad, Sina & Avci, Ibrahim & Kumar, Pushpendra & Baleanu, Dumitru & Rezapour, Shahram, 2022. "Some novel mathematical analysis on the fractal–fractional model of the AH1N1/09 virus and its generalized Caputo-type version," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    4. Yong Wu & Shabir Ahmad & Aman Ullah & Kamal Shah & Nasser Hassen Sweilam, 2022. "Study of the Fractional-Order HIV-1 Infection Model with Uncertainty in Initial Data," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-16, January.
    5. Ravi Agarwal & Snezhana Hristova & Donal O’Regan, 2022. "Generalized Proportional Caputo Fractional Differential Equations with Noninstantaneous Impulses: Concepts, Integral Representations, and Ulam-Type Stability," Mathematics, MDPI, vol. 10(13), pages 1-26, July.
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