Geodesic
On linear conflict-controlled processes with fractional derivatives
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 2, pp. 256-270

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A control problem is considered for quasilinear processes with fractional derivatives under counteraction. Hilfer fractional derivatives are studied, which, in particular, include the classical Riemann–Liouville fractional derivatives and Caputo regularized derivatives. A representation for solutions of such systems is presented, which allows to obtain, using the method of resolving functions, a guaranteed result for the approach of a trajectory to a given target set. Qualitative results are illustrated by an example with the Bagley–Torvik equation, which describes damped oscillations with fractional damping, and by a game problem with the equation of fractional relaxation.
Keywords: game problem, fractional derivative, set-valued mapping, oscillatory process, fractional relaxation. 
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     title = {On linear conflict-controlled processes with fractional derivatives},
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A. A. Chikrii; I. I. Matichin. On linear conflict-controlled processes with fractional derivatives. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 2, pp. 256-270. http://geodesic.mathdoc.fr/item/TIMM_2011_17_2_a20/