Existence and attractivity theorems for nonlinear hybrid fractional differential equations with anticipation and retardation

Abstract

In this paper, we establish an existence result and a global attractivity result for the mild solutions of a nonlinear quadratic hybrid fractional differential equation with the Caputo derivative on the unbounded intervals of the real line with the mixed arguments of anticipation and retardation. The hybrid fixed point theorem of Dhage is used in the analysis of our nonlinear differential problem. A positivity result is also obtained under some usual conditions.