On the Fractional Variable Order Thermostat Model: Existence Theory on Cones via Piece-Wise Constant Functions

Rezapour S., Souid M. S., Bouazza Z., Hussain A., Etemad S.

Journal of Function Spaces, vol.2022, 2022 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 2022
  • Publication Date: 2022
  • Doi Number: 10.1155/2022/8053620
  • Journal Name: Journal of Function Spaces
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, MathSciNet, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Uşak University Affiliated: No

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.