Abstract
By using admissibility theory and fixed point theorems, we studied the existence and uniqueness of random solution of nonlinear fractional stochastic integro-differential equation of Volterra type. In the end, an example is given to show the application of our results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. J. Levin and J. A. Nohel, J. Math. Mech. 9, 347–368 (1960).
R. K. Miller, J. SIAM Appl. Math. 14 (3), 446–452 (1966).
M. N. Oguztoreli, Time Lag Controll Systems (Academic Press, New York, 1966).
Hamdy M. Ahmed, Int. J. of Mathematics and Mathematical Sciences, Article ID 568078, 8 (2009).
Hamdy M. Ahmed, Lobachevskii J. of Mathematics 30 (3), 195–202 (2009).
Hamdy M. Ahmed, J. of Theoretical Probability 26 (4), 667–680 (2013).
Hamdy M. Ahmed, IMA J. of Mathematical Control and Information, doi: 10.1093/imamci/dnu019 (2014).
Hamdy M. Ahmed, Advances in Difference Equations 2014, Article 113 (2014).
W. J. Padgett and C. P. Tosokos, Random Integral Equations with Applications to Stochastic System, Lecture Notes inMathematics (Springer-Verlag, Berlin, 1971), Vol. 233.
P. Balasubramaniam and D. Vinayagam, Computers and Mathematics with Applications 50, 809–821 (2005).
Miljana Jovanovic and Svetlana Jankovic, Filomat 23 (3), 167–180 (2009).
Miljana Jovanovic and Svetlana Jankovic, Filomat 24 (2), 81–92 (2010).
M. G. Murge, Indian J. Pure Appl. Math. 21 (3), 260–274 (1990).
David N. Keck and Mark A. Mckibben, Int. J. of Stochastic Analysis, 1–22 (2006).
W. J. Padgett and C. P. Tosokos, SIAM J. App. Math. 23 (4) (1972).
I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999).
K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations (John Wiley, New York, 1993).
S. Samko, A. Kilbas, and O. L. Marichev, Fractional Integrals and Derivatives (Gordon and Breach Science Publisher, 1993).
R. K. Subramaniam and J. K. Kim, Nonlinear Functional Analysis and Applications 5 (1), 23–29 (2000).
D. Szynal and S. Wedrychowicz, J. of Applied Probability 25 (2), 257–267 (1988).
C. P. Tosokos and W. J. Padgett, Random Integral Equations with Applications to Stochastic Systems, Lecture Notes in Mathematics 233 (Springer, Berlin, Germany, 1971).
C. P. Tosokos and W. J. Padgett, Random Integral Equations with Applications to Life Sciences and Engineering, Mathematics in Science and Engineering 10 (Academic Press, London, UK, 1974).
Author information
Authors and Affiliations
Corresponding author
Additional information
Submitted by A. M. Elizarov
Rights and permissions
About this article
Cite this article
Ahmed, H.M. Solution of nonlinear fractional stochastic integro-differential equation. Lobachevskii J Math 37, 105–113 (2016). https://doi.org/10.1134/S1995080216020025
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995080216020025