JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (10): 13-23.doi: 10.6040/j.issn.1671-9352.0.2019.140

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Existence of mild solutions for a class of fractional stochastic evolution equations with nonlocal initial conditions

CHEN Peng-yu, MA Wei-feng, Ahmed Abdelmonem   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2019-10-12

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Abstract: This paper obtains the existence results of mild solutions to a class of fractional stochastic evolution equations with nonlocal conditions by applying stochastic analysis theory, Schauder fixed point theorem and approximation method assumes that the nonlinear term is Carethéodory continuous and satisfies some weak growth condition, the nonlocal term depends on all the value of independent variable on the whole interval and satisfies some weak growth condition. This work may be viewed as an attempt to develop a general existence theory for fractional stochastic evolution equations with general nonlocal conditions. Finally, as a sample of application, the results are applied to a fractional stochastic partial differential equation with nonlocal integral condition.

Key words: fractional stochastic evolution equations, nonlocal condition, approximation method, compact semigroup, wiener process

CLC Number: 

  • O175.15
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