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Zbl 1081.45007
El-Borai, Mahmoud M.; El-Nadi, Khairia El-Said; Mostafa, Osama L.; Ahmed, Hamdy M.
Volterra equations with fractional stochastic integrals.
(English)
[J] Math. Probl. Eng. 2004, No. 5, 453-468 (2004). ISSN 1024-123X; ISSN 1563-5147/e

Volterra equations with fractional stochastic integrals are considered, where the integrands of the Lebesgue integral and the Ito integral are multiplied by a kernel with a fractional parameter ${\beta}$, respectively. Since the integrands are no more adaptive, the Skorohod integral is used as a tool. Lipschitz-like and local Lipschitz-like conditions are posed on the coefficients to obtain the existence and uniqueness of an adapted solution.
[Gong Guanglu (Beijing)]
MSC 2000:
*45R05 Random integral equations
60H20 Stochastic integral equations
26A33 Fractional derivatives and integrals (real functions)

Keywords: Volterra equation; fractional stochastic integral; Skorokhod integral; existence; uniqueness

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