Existence results for neutral evolution equations with nonlocal conditions and delay via fractional operator

Abstract

In this paper, we study the existence of solutions for the neutral evolution equations with nonlocal conditions and delay in α\alpha -norm, which are more general than in many previous publications. We assume that the linear part generates an analytic semigroup and transforms them into suitable integral equations. By using the Kuratowski measure of noncompactness and fixed-point theory, some existence theorems are established without the assumption of compactness on the associated semigroup. Particularly, our results cover the cases where the nonlinear term FF takes values in different spaces such as Xα{X}_{\alpha }. An example of neutral partial differential system is also given to illustrate the feasibility of our abstract results.

Keywords

• neutral evolution equations
• nonlocal conditions
• nonlocal conditions
• delay
• measure of noncompactness
• α-norm
• 34k30
• 35d35
• 35k55
• 47j35