On the nonlocal Cauchy problem for semilinear fractional order evolution equations

• Autorzy: JinRong Wang , Yong Zhou , Michal Fečkan
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Fractional order evolution equations; Nonlocal Cauchy problem; Mild solution; Existence

Kategorie tematyczne

• 47D06: One-parameter semigroups and linear evolution equations
• 26A33: Fractional derivatives and integrals
• 34G20: Nonlinear equations
• 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 6
• Strony: 911-922

Daty

wydano

2014-06-01

online

2014-03-19

Twórcy

autor

JinRong Wang

autor

Yong Zhou

• Xiangtan University

autor

Michal Fečkan

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0381-y