Coupled fixed point theorems with applications to fractional evolution equations

Abstract

Abstract In this paper, we first prove some coupled fixed point theorems in partially ordered Φ-orbitally complete normed linear spaces. And then apply the obtained fixed point theorems to a class of semilinear evolution systems of fractional order for proving the existence of coupled mild solutions under some weaker monotone conditions. An example is given to illustrate the application of the abstract results.

Keywords

• coupled fixed point theorem
• nonlinear fractional evolution system
• equi-continuous C 0 $C_{0}$ -semigroup
• coupled mild solution
• existence