Volterra equations with fractional stochastic integrals. (English) Zbl 1081.45007

El-Borai, Mahmoud M.; El-Nadi, Khairia El-Said; Mostafa, Osama L.; Ahmed, Hamdy M.

Math. Probl. Eng. 2004, No. 5, 453-468 (2004).

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.

Reviewer: Gong Guanglu (Beijing)

MSC:

45R05	Random integral equations
60H20	Stochastic integral equations
26A33	Fractional derivatives and integrals

Keywords:

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