Geodesic
Differential Games in Fractional-Order Systems: Inequalities for Directional Derivatives of the Value Functional
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal Control and Differential Games, Tome 315 (2021), pp. 74-94

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For a dynamical system described by differential equations with Caputo fractional derivatives of order $\alpha \in (0,1)$, we consider a minimax–maximin differential game with a performance index that estimates the motion of the system on a fixed finite time interval. We obtain differential inequalities that characterize the value functional of the game in terms of appropriate directional derivatives. 
@article{TM_2021_315_a5,
     author = {M. I. Gomoyunov and N. Yu. Lukoyanov},
     title = {Differential {Games} in {Fractional-Order} {Systems:} {Inequalities} for {Directional} {Derivatives} of the {Value} {Functional}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {74--94},
     publisher = {mathdoc},
     volume = {315},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2021_315_a5/}
}
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M. I. Gomoyunov; N. Yu. Lukoyanov. Differential Games in Fractional-Order Systems: Inequalities for Directional Derivatives of the Value Functional. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal Control and Differential Games, Tome 315 (2021), pp. 74-94. http://geodesic.mathdoc.fr/item/TM_2021_315_a5/