Positive solution to fractional thermostat model in Banach spaces via fixed point results

TL;DR

This paper establishes the existence and uniqueness of positive solutions for a fractional thermostat model in Banach spaces using fixed point theorems with altering distance functions, supported by a concrete example.

Contribution

It introduces new fixed point results involving altering distance functions to prove positive solutions for fractional thermostat models in Banach spaces.

Findings

Proved existence and uniqueness of positive solutions for the model.

Developed sufficient conditions based on fixed point theorems.

Provided a non-trivial example validating the theoretical results.

Abstract

The motive behind this manuscript is to set up the existence and uniqueness of a positive solution for a fractional thermostat model for certain values of the parameter $\lambda>0$. We accomplish sufficient conditions for the existence of a positive solution to the model, and afterwards formulate a non-trivial example to authenticate the grounds of our obtained results. Our findings are based on certain fixed point results of contractions depending on couple of altering distance functions $\phi$ and $\psi$ in the setting of Banach spaces that are discussed in this sequel.