# American Institute of Mathematical Sciences

February  2018, 11(1): 59-76. doi: 10.3934/dcdss.2018004

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

 1 Department of Applied Mathematics, School of Mathematics and Computer Science, Damghan University, Damghan, Iran 2 Center for Research & Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

* Corresponding author: Delfim F. M. Torres

Received  June 2016 Revised  November 2016 Published  January 2018

Fund Project: This work is part of second author's PhD project. It was partially supported by Damghan University, Iran; and CIDMA-FCT, Portugal, under project UID/MAT/04106/2013.

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.

Citation: Omid S. Fard, Javad Soolaki, Delfim F. M. Torres. A necessary condition of Pontryagin type for fuzzy fractional optimal control problems. Discrete & Continuous Dynamical Systems - S, 2018, 11 (1) : 59-76. doi: 10.3934/dcdss.2018004
##### References:

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##### References:
The fuzzy extremals for the fuzzy optimal control problem (12) of Example 1 under $[(1)-gH]_{\beta}^{C}$-differentiability of $\tilde{x}$
The fuzzy extremals for the fuzzy optimal control problem (12) of Example 1 under $[(2)-gH]$-differentiability of $\tilde{x}$
The extremals for the crisp optimal control problem (19) of Example 2
The fuzzy extremals for the fuzzy optimal control problem (18) of Example 2
The extremals for the crisp optimal control problem (22) of Example 3
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