Analysis of fractional integro-differential equations of thermistor type

TL;DR

This paper surveys fractional differential equations, focusing on thermistor-type equations, discussing various fractional operators, and establishing existence and uniqueness of solutions using fixed-point theorems.

Contribution

It provides a comprehensive review of methods and results for fractional thermistor equations, including existence, uniqueness, and continuation of solutions.

Findings

Existence and uniqueness of positive solutions established.

Global existence results provided.

Analysis includes Riemann-Liouville, Caputo, and time-scale fractional operators.

Abstract

We survey methods and results of fractional differential equations in which an unknown function is under the operation of integration and/or differentiation of fractional order. As an illustrative example, we review results on fractional integral and differential equations of thermistor type. Several nonlocal problems are considered: with Riemann-Liouville, Caputo, and time-scale fractional operators. Existence and uniqueness of positive solutions are obtained through suitable fixed-point theorems in proper Banach spaces. Additionally, existence and continuation theorems are given, ensuring global existence.