Well-posedness and regularity of some stochastic time-fractional integral equations in Hilbert space

Arab Z., Tunç C.

JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE, vol.16, no.1, pp.788-798, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.1080/16583655.2022.2119587
  • Journal Name: JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.788-798
  • Keywords: Integral equations, Riemann-Liouville integral operator, cylindrical Wiener process, fixed point theorem, spatial regularity, temporal regularity, INTEGRODIFFERENTIAL EQUATIONS, OPTICAL SOLITONS, STABILITY, DRIVEN
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In the current work, we deal with a class of stochastic time-fractional integral equations in Hilbert space by studying their well-posedness and regularity. Precisely, we use the celebrity fixed point theorem to prove the well-posedness of the problem by imposing the global Lipschitz and the linear growth conditions. Further, we prove the spatial and temporal regularity by imposing only a regularity condition on the initial value. An important example is considered in order to confirm and support the validity of our theoretical results.