Skip to main content
SpringerLink
Log in
Book cover

Mathematical Analysis and its Applications pp 373–380Cite as

Existence of Solution for Fractional Stochastic Integro-Differential Equation with Impulsive Effect

  • Conference paper
  • First Online:

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 143))

Abstract

This paper is concerned with the existence and uniqueness of the solution for an impulsive fractional stochastic integro-differential equation. The existence and uniqueness results are shown using the fixed point technique on a Hilbert space.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Chauhan, A., Dabas, J.: Existence of mild solutions for impulsive fractional-order semilinear evolution equations with nonlocal conditions. Electron. J. Differ. Equ. 2011(107), 1–10 (2011)

    MathSciNet  Google Scholar 

  2. Chauhan, A., Dabas, J.: Local and global existence of mild solution to an impulsive fractional functional integro-differential equation with nonlocal condition. Commun. Nonlinear. Sci. Numer. Simulat. 19, 821–829 (2014)

    Article  MathSciNet  Google Scholar 

  3. Chauhan, A., Dabas, J., Kumar, M.: Integral boundary-value problem for impulsive fractional functional differential equations with infinite delay. Electron. J. Differ. Equ. 2012(229), 1–13 (2012)

    MathSciNet  MATH  Google Scholar 

  4. Dabas, J., Chauhan, A.: Existence and uniqueness of mild solution for an impulsive neutral fractional integro-differential equation with infinite delay. Math. Comput. Model. 57, 754–763 (2013)

    Article  MathSciNet  Google Scholar 

  5. Dabas, J., Chauhan, A., Kumar, M.: Existence of the mild solutions for impulsive fractional equations with infinite delay. Intern. J. Differ. Equ. 793023, 20 (2011)

    MathSciNet  Google Scholar 

  6. Dabas, J., Gautam, G.R.: Impulsive neutral fractional integro-differential equations with state dependent delays and integral conditions. Electron. J. Differ. Equ. 2013(273), 1–13 (2013)

    MathSciNet  Google Scholar 

  7. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier Science B.V, Amsterdam (2006)

    MATH  Google Scholar 

  8. Lakshmikantham, V.: Theory of fractional differential equations. Nonlinear Anal. 69, 3337–3343 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Lakshmikantham, V., Bainov, D., Simeonov, P.: Theory of Impulsive Differential Equations. World Scientific Press, Singapore (1989)

    Book  MATH  Google Scholar 

  10. Li, C., Sun, J., Sun, R.: Stability analysis of a class of stochastic differential delay equations with nonlinear impulsive effects. J. Franklin Inst. 347, 1186–1198 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Lin, A., Ren, Y., Xia, N.: On neutral impulsive stochastic integro-differential equations with infinite delays via fractional operators. Math. Comput. Model. 51, 413–424 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. Longa, S., Teng, L., Xu, D.: Global attracting set and stability of stochastic neutral partial functional differential equations with impulses. Stat. Probab. Lett. 82, 1699–1709 (2012)

    Article  Google Scholar 

  13. Oksendal, B.: Stochastic Differential Equations. Springer, Berlin, Heidelberg (2005)

    Google Scholar 

  14. Podlubny, I.: Fractional Differential Equations. Acadmic Press, New York, USA (1993)

    Google Scholar 

  15. Sakthivel, R., Revathi, P., Ren, Y.: Existence of solutions for nonlinear fractional stochastic differential equations. Nonlilear Anal. 81, 70–86 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  16. Wang, J.R., Li, X., Wei, W.: On the natural solution of an impulsive fractional differential equation of order \(\alpha \in (1,2)\). Commun. Nonlinear Sci. Numer. Simulat. 17, 4384–4394 (2012)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Science and Engineering, IIT Roorkee, Saharanpur Campus, Saharanpur, 247001, India

    Mohd Nadeem & Jaydev Dabas

Authors
  1. Mohd Nadeem
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jaydev Dabas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohd Nadeem .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    P. N. Agrawal

  2. Department of Mathematics, University of Central Florida, Orlando, Florida, USA

    R. N. Mohapatra

  3. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Uaday Singh

  4. Dept. of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada

    H. M. Srivastava

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer India

About this paper

Cite this paper

Nadeem, M., Dabas, J. (2015). Existence of Solution for Fractional Stochastic Integro-Differential Equation with Impulsive Effect. In: Agrawal, P., Mohapatra, R., Singh, U., Srivastava, H. (eds) Mathematical Analysis and its Applications. Springer Proceedings in Mathematics & Statistics, vol 143. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2485-3_30

Download citation

Publish with us

Policies and ethics

Search

Navigation