On the Fractional Variable Order Thermostat Model: Existence Theory on Cones via Piece-Wise Constant Functions. (24th March 2022)

• Record Type: Journal Article
• Authors: Rezapour, Shahram; Souid, Mohammed Said; Bouazza, Zoubida; Hussain, Azhar; Etemad, Sina
• Other Names: Scapellato Andrea Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2022(2022)
• Publication Date: 2022-03-24
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2022/8053620
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In the current manuscript, we intend to investigate the existence, uniqueness, and the stability of positive solution in relation to a fractional version of variable order thermostat model equipped with nonlocal boundary values in the Caputo sense. In fact, we will get help from the constant piece-wise functions for transforming our variable order model into an auxiliary standard model of thermostat. By Guo-Krasnoselskii's fixed point theorem on cones, we derive the required conditions ensuring the existence property for positive solutions. An example is illustrated to examine the validity of the observed results.