Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solution to Zero-Sum Differential Game with Fractional Dynamics via
  Approximations   The paper deals with a zero-sum differential game in which the dynamical
system is described by a fractional differential equation with the Caputo
derivative of an order $\alpha \in (0, 1).$ The goal of the first (second)
player is to minimize (maximize) the value of a given quality index. The main
contribution of the paper is the proof of the fact that this differential game
has the value, i.e., the lower and upper game values coincide. The proof is
based on the appropriate approximation of the game by a zero-sum differential
game in which the dynamical system is described by a first order functional
differential equation of a retarded type. It is shown that the values of the
approximating differential games have a limit, and this limit is the value of
the original game. Moreover, the optimal players' feedback control procedures
are proposed that use the optimally controlled approximating system as a guide.

26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat