This paper is devoted to study the existence of mild solutions for semilinear
functional differential equations with state-dependent delay involving the
Riemann-Liouville fractional derivative in a Banach space and resolvent
operator. The arguments are based upon M?nch?s fixed point theoremand the
technique of measure of noncompactness.
This chapter presents a selection of some of the most important results in the theory of Sobolev spacesn. Special emphasis is placed on embedding theorems and the question as to whether an embedding map is compact or not. Some results concerning the k-set contraction nature of certain embedding maps are given, for both bounded and unbounded space domains: also the approximation numbers of embedding maps are estimated and these estimates used to classify the embeddings.
AbstractIn this paper we prove the existence and uniqueness of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay in Banach spaces. We generalize the existence theorem for integer order differential equations to the fractional order case. The results obtained here improve and generalize many known results.
Existence and Uniqueness of Mild Solutions for the Damped Burgers Equation in Weighted Sobolev Spaces on the Half Line