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

Shahram Rezapour, Sina Etemad, Ravi P. Agarwal and Kamsing Nonlaopon ()
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Shahram Rezapour: Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran
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

Mathematics, 2022, vol. 10, issue 21, 1-11

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.

Keywords: boundary value problem; Lyapunov inequality; generalized fractional operator; thermostat model; non-existence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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