# Optimal control of a nonlocal thermistor problem with ABC fractional time derivatives

## TL;DR

This paper investigates an optimal control problem for a fractional nonlocal thermistor model using ABC fractional derivatives, establishing solution existence, uniqueness, and optimality conditions.

## Contribution

It introduces a novel optimal control framework for thermistor problems with ABC fractional derivatives, including existence, uniqueness, and optimality system derivation.

## Key findings

- Existence and uniqueness of solutions proven.
- Optimal control existence established.
- Optimality system derived.

## Abstract

We study an optimal control problem associated to a fractional nonlocal thermistor problem involving the ABC (Atangana-Baleanu-Caputo) fractional time derivative. We first prove the existence and uniqueness of solution. Then, we show that an optimal control exists. Moreover, we obtain the optimality system that characterizes the control.