**4. Conclusions**

In this paper we investigated fractional optimal control problems depending on distributed-order fractional operators. We have proven a necessary optimality condition of Pontryagin's type and a Mangasarian-type sufficient optimality condition. The new results were illustrated with an example. As for future work, it would be interesting to develop proper numerical approaches to solve problems of optimal control with distributed-order fractional derivatives. In this direction, the approaches found in [17,18] can be easily adapted.

**Author Contributions:** The authors equally contributed to this paper, read and approved the final manuscript: Formal analysis, F.N. and D.F.M.T.; Investigation, F.N. and D.F.M.T.; Writing—original draft, F.N. and D.F.M.T.; Writing—review and editing, F.N. and D.F.M.T. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Portuguese Foundation for Science and Technology (FCT), gran<sup>t</sup> number UIDB/04106/2020 (CIDMA). Ndaïrou was also supported by FCT through the PhD fellowship PD/BD/150273/2019.

**Acknowledgments:** The authors are grateful to two anonymous reviewers for several comments and suggestions that have helped them to improve the manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.
