×

On some fractional stochastic integrodifferential equations in Hilbert space. (English) Zbl 1179.60038

Summary: We study a class of fractional stochastic integrodifferential equations considered in a real Hilbert space. The existence and uniqueness of the Mild solutions of the considered problem is also studied. We also give an application for stochastic integropartial differential equations of fractional order.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H20 Stochastic integral equations
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] D. N. Keck and M. A. McKibben, “Functional integro-differential stochastic evolution equations in Hilbert space,” Journal of Applied Mathematics and Stochastic Analysis, vol. 16, no. 2, pp. 141-161, 2003. · Zbl 1031.60061 · doi:10.1155/S1048953303000108
[2] M. M. El-Borai, K. El-Said El-Nadi, O. L. Mostafa, and H. M. Ahmed, “Semigroup and some fractional stochastic integral equations,” International Journal Pure and Applied Mathematical Science, vol. 3, no. 1, pp. 47-52, 2006.
[3] D. Bahuguna, “Integro-differential equations with analytic semigroup,” Journal of Applied Mathematics and Stochastic Analysis, vol. 16, no. 2, pp. 177-189, 2003. · Zbl 1047.34069 · doi:10.1155/S1048953303000133
[4] D. Bahuguna, “Quasi linear integro-differential equations in Banach spaces,” Nonlinear Analysis, vol. 24, pp. 175-183, 1995. · Zbl 0823.45010 · doi:10.1016/0362-546X(94)E0049-M
[5] D. Bahuguna and A. K. Pani, “Strong solutions to nonlinear integro-differential equations,” Research Report CMA-R 29-90, Australian National University, Canberra, Australia, 1990.
[6] M. M. El-Borai, “Semigroups and some nonlinear fractional differential equations,” Applied Mathematics and Computation, vol. 149, no. 3, pp. 823-831, 2004. · Zbl 1046.34079 · doi:10.1016/S0096-3003(03)00188-7
[7] M. M. El-Borai, “On some fractional differential equations in the Hilbert space,” Discrete and Continuous Dynamical Systems. Series A, pp. 233-240, 2005. · Zbl 1160.47038
[8] M. M. El-Borai, “Some probability densities and fundamental solutions of fractional evolution equations,” Chaos, Solitons and Fractals, vol. 14, no. 3, pp. 433-440, 2002. · Zbl 1005.34051 · doi:10.1016/S0960-0779(01)00208-9
[9] M. M. El-Borai, K. El-Said El-Nadi, O. L. Mostafa, and H. M. Ahmed, “Volterra equations with fractional stochastic integrals,” Mathematical Problems in Engineering, vol. 2004, no. 5, pp. 453-468, 2004. · Zbl 1081.45007 · doi:10.1155/S1024123X04312020
[10] M. M. El-Borai, “The fundamental solutions for fractional evolution equations of parabolic type,” Journal of Applied Mathematics and Stochastic Analysis, vol. 2004, no. 3, pp. 197-211, 2004. · Zbl 1081.34053 · doi:10.1155/S1048953304311020
[11] W. Feller, An Introduction to Probability Theory and Its Applications. Vol. II., 2nd, John Wiley & Sons, New York, NY, USA, 1971. · Zbl 0219.60003
[12] R. Gorenflo and F. Mainardi, “Fractional calculus and stable probability distributions,” Archives of Mechanics, vol. 50, no. 3, pp. 377-388, 1998. · Zbl 0934.35008
[13] T. E. Govidan, “Autonomous semi linear stochastic Volterra itegro-differential equations in Hilbert spaces,” Dynamic Systems and Applications, vol. 3, pp. 51-74, 1994.
[14] T. E. Govidan, Stability of Stochastic Differential Equations in a Banach Space, Mathematical Theory of Control, Lecture Notes in Pure and Applied Mathematics, 142, Marcel-Dekker, New York, NY, USA, 1992.
[15] W. Grecksch and C. Tudor, Stochastic Evolution Equations: A Hilbert Space Approach, vol. 85 of Mathematical Research, Akademie, Berlin, Germany, 1995. · Zbl 0831.60069
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.