# Existence and uniqueness results for a fractional Riemann-Liouville nonlocal thermistor problem on arbitrary time scales

## TL;DR

This paper establishes the existence and uniqueness of positive solutions for a fractional Riemann-Liouville nonlocal thermistor problem on arbitrary time scales using fixed point theory.

## Contribution

It introduces new existence and uniqueness results for a fractional thermistor problem on arbitrary time scales, expanding the scope of previous studies.

## Key findings

- Proves positive solutions exist and are unique under certain conditions.
- Applies fixed point theorem in Banach space to fractional nonlocal problems.
- Extends thermistor problem analysis to arbitrary time scales.

## Abstract

Using a fixed point theorem in a proper Banach space, we prove existence and uniqueness results of positive solutions for a fractional Riemann-Liouville nonlocal thermistor problem on arbitrary nonempty closed subsets of the real numbers.