Skip to main content
SpringerLink
Log in

Semilinear Neutral Fractional Stochastic Integro-Differential Equations with Nonlocal Conditions

  • Published:
Journal of Theoretical Probability Aims and scope Submit manuscript

Abstract

In this paper, we prove the existence of mild solutions for a class of semilinear neutral fractional stochastic integro-differential equations with nonlocal conditions. Sufficient conditions for the existence are derived with the help of the Sadovskii fixed point theorem. 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.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Mao, X.: Stochastic Differential Equations and Applications. Horwood, Chichester (1997)

    Google Scholar 

  2. Protter, P.: Stochastic Integration and Differential Equations. Applications of Mathematics. Springer, Berlin (1990)

    Book  Google Scholar 

  3. Sobczyk, K.: Stochastic Differential Equations with Applications to Physics and Engineering. Kluwer, London (1991)

    Google Scholar 

  4. Byszewski, L., Lakshmikantham, V.: Theorem about the existence and uniqueness of a solution of a nonlocal Cauchy problem in a Banach space. Appl. Anal. 40, 11–19 (1990)

    Article  MathSciNet  Google Scholar 

  5. Byszewski, L.: Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem. J. Math. Anal. Appl. 162, 494–506 (1991)

    Article  MathSciNet  Google Scholar 

  6. Byszewski, L.: Existence and uniqueness of solutions of semilinear evolution nonlocal Cauchy problem. Zeszyty Nauk. Rzeszowskiej Mat. Fiz. 18, 109–112 (1993)

    MathSciNet  Google Scholar 

  7. Boucherif, A., Precup, R.: Semilinear evolution equations with nonlocal initial conditions. Dyn. Syst. Appl. 16(3), 507–516 (2007)

    MathSciNet  Google Scholar 

  8. Liang, J., Xiao, T.-J.: Semilinear integrodifferential equations with nonlocal initial conditions. Comput. Math. Appl. 47(6–7), 863–875 (2004)

    Article  MathSciNet  Google Scholar 

  9. Boucherif, A.: Semilinear evolution inclusions with nonlocal conditions. Appl. Math. Lett. 22(8), 1145–1149 (2009)

    Article  MathSciNet  Google Scholar 

  10. Hale, J., Verduyn, L., Sjoerd, M.: Introduction to Functional Differential Equations, Applied Mathematical Sciences, vol. 99. Springer, New York (1993)

    Book  Google Scholar 

  11. Kolmanovskii, V.B., Myshkis, A.: Applied Theory of Functional Differential Equations. Kluwer, Dordrecht (1992)

    Book  Google Scholar 

  12. El-Borai, M.M.: On some stochastic fractional integro-differential equations. Adv. Dyn. Syst. Appl. 1, 49–57 (2006)

    MathSciNet  Google Scholar 

  13. Ahmed, H.M.: On some fractional stochastic integrodifferential equations in Hilbert spaces. Int. J. Math. Math. Sci. 2009, Article ID 568078, 8 pages, (2009)

  14. Cui, J., Yan, L.: Existence result for fractional neutral stochastic integro-differential equations with infinite delay. J. Phys. A Math. Theor. 44, 335201 (2011)

    Article  MathSciNet  Google Scholar 

  15. Sakthivel, R., Revathi, P., Marshal Anthoni, S.: Existence of pseudo almost automorphic mild solutions to stochastic fractional differential equations. Nonlinear Anal. 75, 3339–3347 (2012)

    Article  MathSciNet  Google Scholar 

  16. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)

    Google Scholar 

  17. Miller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York (1993)

    Google Scholar 

  18. Samko, S., Kilbas, A., Marichev, O.L.: Fractional Integrals and Derivatives. Gordon and Breach Science Publisher, London (1993)

    Google Scholar 

  19. Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, vol. 44. Springer, New York (1983)

    Book  Google Scholar 

  20. Sadovskii, B.N.: On a fixed point principle. Funct. Anal. Appl. 1, 71–74 (1967)

    Google Scholar 

  21. Zhou, Y., Jiao, F., Li, J.: Existence of mild solutions for fractional neutral evolution equations. Comput. Math. Appl. 59, 1063–1077 (2010)

    Article  MathSciNet  Google Scholar 

  22. Marle, C.M.: Measures et Probabilités. Hermann, Paris (1974)

    Google Scholar 

Download references

Acknowledgments

I would like to thank the referees for their valuable comments and suggestions.

Author information

Authors and Affiliations

  1. Higher Institute of Engineering, El-Shorouk Academy, P.O. 3, El-Shorouk City, Cairo, Egypt

    Hamdy M. Ahmed

Authors
  1. Hamdy M. Ahmed
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hamdy M. Ahmed.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ahmed, H.M. Semilinear Neutral Fractional Stochastic Integro-Differential Equations with Nonlocal Conditions. J Theor Probab 28, 667–680 (2015). https://doi.org/10.1007/s10959-013-0520-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10959-013-0520-1

Keywords

Mathematics Subject Classification (2010)

Search

Navigation