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

• * Corresponding author: Delfim F. M. Torres
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.

Mathematics Subject Classification: Primary: 26A33, 93C42; Secondary: 49K05.

 Citation:

• Figure 1.  The fuzzy extremals for the fuzzy optimal control problem (12) of Example 1 under $[(1)-gH]_{\beta}^{C}$-differentiability of $\tilde{x}$

Figure 2.  The fuzzy extremals for the fuzzy optimal control problem (12) of Example 1 under $[(2)-gH]$-differentiability of $\tilde{x}$

Figure 3.  The extremals for the crisp optimal control problem (19) of Example 2

Figure 4.  The fuzzy extremals for the fuzzy optimal control problem (18) of Example 2

Figure 5.  The extremals for the crisp optimal control problem (22) of Example 3

Figures(5)