On solutions of some delay Volterra integral problems on a half-line

Abstract

In this paper, we study the existence of a.e. monotonic solutions of some general delay integral problems for both fractional and integer orders in the space of Lebesgue integrable functions on the interval R+ = [0;1) and in the space of locally integrable functions L1loc (R+). In particular, the uniqueness of solutions for considered problems is obtained.

Keywords

• superposition operator
• Carathéodory conditions
• measure of noncompactness
• delay integral equations
• Darbo fixed point theorem