# A necessary condition of Pontryagin type for fuzzy fractional optimal control problems

## TL;DR

This paper establishes necessary Pontryagin-type optimality conditions for fuzzy fractional control problems involving Caputo derivatives, enhancing previous results and demonstrating the conditions through three illustrative examples.

## Contribution

It introduces new necessary conditions for fuzzy fractional optimal control problems with Caputo derivatives, extending existing theoretical frameworks.

## Key findings

- Derived Pontryagin-type conditions for fuzzy fractional control
- Improved upon recent results by Najariyan and Farahi
- Validated conditions with three example systems

## Abstract

We prove necessary optimality conditions of Pontryagin type for a class of fuzzy fractional optimal control problems with the fuzzy fractional derivative described in the Caputo sense. The new results are illustrated by computing the extremals of three fuzzy optimal control systems, which improve recent results of Najariyan and Farahi.