# On the nonlocal Cauchy problem for semilinear fractional order evolution equations

Open Mathematics (2014)

• Volume: 12, Issue: 6, page 911-922
• ISSN: 2391-5455

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## Abstract

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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.

## How to cite

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JinRong Wang, Yong Zhou, and Michal Fečkan. "On the nonlocal Cauchy problem for semilinear fractional order evolution equations." Open Mathematics 12.6 (2014): 911-922. <http://eudml.org/doc/269554>.

@article{JinRongWang2014,
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.},
author = {JinRong Wang, Yong Zhou, Michal Fečkan},
journal = {Open Mathematics},
keywords = {Fractional order evolution equations; Nonlocal Cauchy problem; Mild solution; Existence; fractional order evolution equations; nonlocal Cauchy problem; mild solution; existence},
language = {eng},
number = {6},
pages = {911-922},
title = {On the nonlocal Cauchy problem for semilinear fractional order evolution equations},
url = {http://eudml.org/doc/269554},
volume = {12},
year = {2014},
}

TY - JOUR
AU - JinRong Wang
AU - Yong Zhou
AU - Michal Fečkan
TI - On the nonlocal Cauchy problem for semilinear fractional order evolution equations
JO - Open Mathematics
PY - 2014
VL - 12
IS - 6
SP - 911
EP - 922
AB - 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.
LA - eng
KW - Fractional order evolution equations; Nonlocal Cauchy problem; Mild solution; Existence; fractional order evolution equations; nonlocal Cauchy problem; mild solution; existence
UR - http://eudml.org/doc/269554
ER -

## References

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