On fractional integro-differential inclusions with state-dependent delay in Banach spaces

Abstract

In this article we investigate the existence of solutions on a compact interval for the fractional integro-differential inclusions with state-dependent delay in Banach spaces when the delay is infinite. We consider the cases when the multivalued nonlinear term takes convex values as well as nonconvex values.

Keywords:

• differential inclusions
• integral resolvent family
• mild solution
• fixed points
• state-dependent delay
• infinite delay

AMS Subject Classifications::

• 26A30
• 34A60
• 34G20
• 34G25