Initial value problem for fractional evolution equations

• Published in: Advances in difference equations Vol. 2012; no. 1; pp. 1 - 10
• Main Authors: Fan, Hongxia, Mu, Jia
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 19.04.2012; Springer Nature B.V; BioMed Central Ltd
• Subjects: Analysis; Classification; Condensing; Difference and Functional Equations; Difference equations; Evolution; Existence theorems; Functional Analysis; Initial value problems; Mathematical analysis; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; fractional evolution equations; mild solutions; condensing maps; initial value problem; measure of noncompactness

This article is concerned with the existence of mild solutions to the initial value problem for a class of semilinear evolution equations with fractional order. New existence theorems are obtained by means of fixed point theorem for condensing maps. The results extend some related results in this di...