Qualitative properties and approximate solutions of thermostat fractional dynamics system via a nonsingular kernel operator

Purpose This paper aims to study qualitative properties and approximate solutions of a thermostat dynamics system with three-point boundary value conditions involving nonsingular kernel operator which is called Atangana-Baleanu-Caputo (ABC) derivative for the first time. The results existence uniqueness solution such are investigated minimum hypotheses by employing Banach Schauder's fixed point theorems. Furthermore, Ulam-Hyers (UH) stability, Ulam-Hyers-Rassias xmlns:m="http://www.w3.org/1998/Math/MathML">UHR stability their generalizations discussed using some topics concerning nonlinear functional analysis. An efficiency Adomian decomposition method (ADM) established in order estimate our problem convergence theorem proved. Finally, four examples exhibited illustrate validity theoretical numerical results. Design/methodology/approach considered methodologies. Findings contains following findings: (1) Thermostat fractional studied under ABC operator. (2) Qualitative as existence, Ulam–Hyers–Rassias theorems analysis topics. (3) Approximate Adomain method. (4) Convergence ADM (5) Examples provided (6) Numerical compared exact tables figures. Originality/value novelty contributions this use time system.