On the qualitative analysis of the fractional boundary value problem describing thermostat control model via ψ-Hilfer fractional operator

Advances in Difference Equations

Weerawat Sudsutad¹  Jehad Alzabut²  Sina Etemad³  Shahram Rezapour⁴  Chatthai Thaiprayoon⁵ 

[1] Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, 10800, Bangkok, Thailand;Department of Mathematics and General Sciences, Prince Sultan University, 11586, Riyadh, Saudi Arabia;Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran;Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran;Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan;Department of Mathematics, Faculty of Science, Burapha University, 20131, Chonburi, Thailand;

关键词: ψ;    Existence of solutions;    Fixed point;    Ulam–Hyers stability;    Uniqueness;    Thermostat control model;    34A08;    34A12;    39B10;   

DOI  :  10.1186/s13662-021-03359-z

来源: Springer

【 摘 要 】

In this research study, we are concerned with the existence and stability of solutions of a boundary value problem (BVP) of the fractional thermostat control model with ψ-Hilfer fractional operator. We verify the uniqueness criterion via the Banach fixed-point principle and establish the existence by using the Schaefer and Krasnoselskii fixed-point results. Moreover, we apply the arguments related to the nonlinear functional analysis to discuss various types of stability in the format of Ulam. Finally, by several examples we demonstrate applications of the main findings.

【 授权许可】

CC BY