On maximal and minimal solutions for set integro-differential equations with feedback control

Abstract

In this paper, a class of new set-valued differential equations on semilinear Hausdorff space under classic Hukuhara derivative, called set-valued integro-differential equations (SCIDEs) which is developed under the form $D_H X\left( t \right) = F\left( {t,X\left( t \right), U(t),\int\limits_{t_0 }^t {G\left( {t,s,X\left( s \right),U(s)} \right)ds} } \right)$. Moreover, some corresponding properties of SCIDE are discussed such as existence, uniqueness, bounded of solutions. Beside that,the existence maximal and minimal solutions for SCIDE with feedback controls are presented.