On the nonlocal Cauchy problem for semilinear fractional order evolution equations

JinRong Wang ; Yong Zhou ; Michal Fečkan

Open Mathematics, Tome 12 (2014), p. 911-922 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Détail

Publié le : 2014-01-01

Zbl 1296.26035

EUDML-ID : urn:eudml:doc:269554

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