Existence results for fractional integro-differential inclusions with state-dependent delay

Abstract

In this paper we are concerned with a class of abstract fractional integro-differential inclusions with infinite state-dependent delay. Our approach is based on the existence of a resolvent operator for the homogeneous equation.We establish the existence of mild solutions using both contractive maps and condensing maps. Finally, an application to the theory of heat conduction in materials with memory is given.

Keywords

• fractional integral-differential inclusion
• multi-valued maps
• resolvent operator
• state-dependent delay
• primary 34k37
• 34g25. secondary 34k30
• 34k09