Quasilinear integral games of approach

Abstract

Integral games of approach are considered in which the dynamics of a process under consideration is described by Volterra integral equations of second order with kernels having polar summable peculiarities. These games are connected naturally with the important class of model integral equations, solutions of which are expressed in terms of the generalized Mittag-Leffler function E/sub /spl rho//(z;/spl mu/)=/spl infin//spl Sigma//spl kappa/=0 z/sup /spl kappa////spl Gamma/(/spl mu/+/spl kappa//sub /spl rho///sup -1/), where /spl Gamma/(a) is the Euler gamma-function. This fact and the in-depth study of the asymptotic behavior of E/sub /spl rho//(Z;/spl mu/) (as z/spl rarr//spl infin/), given in Dzharbashyan (1966), makes it possible to derive the formulas for solution of the problem under consideration for a rather broad class of model games.