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On the nonlocal Cauchy problem for semilinear fractional order evolution equations

✍ Scribed by Wang, JinRong ;Zhou, Yong ;Fečkan, Michal

Book ID
121552101
Publisher
Walter de Gruyter GmbH
Year
2014
Tongue
English
Weight
994 KB
Volume
12
Category
Article
ISSN
2391-5455

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✦ Synopsis

Abstract

In this paper, we develop the approach and techniques of [Boucherif A., Precup R., Semilinear evolution equations with nonlocal initial conditions, Dynam. Systems Appl., 2007, 16(3), 507–516], [Zhou Y., Jiao F., Nonlocal Cauchy problem for fractional evolution equations, Nonlinar Anal. Real World Appl., 2010, 11(5), 4465–4475] to deal with nonlocal Cauchy problem for semilinear fractional order evolution equations. We present two new sufficient conditions on existence of mild solutions. The first result relies on a growth condition on the whole time interval via Schaefer fixed point theorem. The second result relies on a growth condition splitted into two parts, one for the subinterval containing the points associated with the nonlocal conditions, and the other for the rest of the interval via O’Regan fixed point theorem.

📜 SIMILAR VOLUMES

Nonlocal Cauchy problem for fractional e
Nonlocal Cauchy problem for fractional evolution equations
✍ Yong Zhou; Feng Jiao 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 333 KB

In this paper, the nonlocal Cauchy problem is discussed for the fractional evolution equations in an arbitrary Banach space and various criteria on the existence and uniqueness of mild solutions are obtained. An example to illustrate the applications of main results is also given.