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• W4319162102 abstract "Purpose This paper aims to study qualitative properties and approximate solutions of a thermostat dynamics system with three-point boundary value conditions involving a nonsingular kernel operator which is called Atangana-Baleanu-Caputo (ABC) derivative for the first time. The results of the existence and uniqueness of the solution for such a system are investigated with minimum hypotheses by employing Banach and Schauder's fixed point theorems. Furthermore, Ulam-Hyers <m:math xmlns:m=http://www.w3.org/1998/Math/MathML><m:mo>(</m:mo><m:mi mathvariant=script>UH</m:mi><m:mo>)</m:mo></m:math> stability, Ulam-Hyers-Rassias <m:math xmlns:m=http://www.w3.org/1998/Math/MathML><m:mi mathvariant=script>UHR</m:mi></m:math> stability and their generalizations are discussed by using some topics concerning the nonlinear functional analysis. An efficiency of Adomian decomposition method (ADM) is established in order to estimate approximate solutions of our problem and convergence theorem is proved. Finally, four examples are exhibited to illustrate the validity of the theoretical and numerical results. Design/methodology/approach This paper considered theoretical and numerical methodologies. Findings This paper contains the following findings: (1) Thermostat fractional dynamics system is studied under ABC operator. (2) Qualitative properties such as existence, uniqueness and Ulam–Hyers–Rassias stability are established by fixed point theorems and nonlinear analysis topics. (3) Approximate solution of the problem is investigated by Adomain decomposition method. (4) Convergence analysis of ADM is proved. (5) Examples are provided to illustrate theoretical and numerical results. (6) Numerical results are compared with exact solution in tables and figures. Originality/value The novelty and contributions of this paper is to use a nonsingular kernel operator for the first time in order to study the qualitative properties and approximate solution of a thermostat dynamics system." @default.
• W4319162102 created "2023-02-04" @default.
• W4319162102 creator A5023573264 @default.
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• W4319162102 date "2023-02-03" @default.
• W4319162102 modified "2023-10-09" @default.
• W4319162102 title "Qualitative properties and approximate solutions of thermostat fractional dynamics system via a nonsingular kernel operator" @default.
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• W4319162102 doi "https://doi.org/10.1108/ajms-06-2022-0147" @default.
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