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

Arab Z., Tunç C.

JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE, cilt.16, sa.1, ss.788-798, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 16 Sayı: 1
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1080/16583655.2022.2119587
  • Dergi Adı: JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.788-798
  • Anahtar Kelimeler: 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 Üniversitesi Adresli: Evet

Özet

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.