Skip to main content
SpringerLink
Log in

On Some Approximate Solutions of Nonlinear Integrodifferential Equation on Time Scales

  • Original Research
  • Published:
Differential Equations and Dynamical Systems Aims and scope Submit manuscript

Abstract

The main objective of the paper is to study the approximate solutions of certain dynamic nonlinear integrodifferential equations on time scales which unifies the study of corresponding continuous and discrete version of the same. A new integral inequality with explicit estimates are used to establish the 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. Bohner M., Peterson A.: Dynamic Equations on Time Scales. Birkhauser, Boston (2001)

    Book  MATH  Google Scholar 

  2. Bohner M., Peterson A.: Advances in Dynamic Equations on Time Scales. Birkhauser, Boston (2003)

    Book  MATH  Google Scholar 

  3. Bohner, E.A., Bohner, M., Akin, F.: Pachpatte inequalities on time scale. J. Inequal. Pure. Appl. Math 6(1) Art 6.(2005)

  4. Hilger S.: Analysis on measure chain-A unified approch to continuous and discrete calculus. Results Math. 18, 18–56 (1990)

    MathSciNet  MATH  Google Scholar 

  5. Kulik T., Tisdell C.C.: Volterra integral equations on time scales: basic qualitative and quantitative results with applications to initial value problems on unbounded domains. Int. J. Difference Equ. 3(1), 103–133 (2008)

    MathSciNet  Google Scholar 

  6. Pachpatte, D.B.: Explicit estimates on integral inequalities with time scale. J. Inequal. Pure Appl. Math. 7(4), Artivle 143,(2006)

    Google Scholar 

  7. Pachpatte D.B.: On approximate solutions of a volterra type integrodifferential equations on time scales, Int. J. Math. Anal. 4(34), 1651–1659 (2010)

    MATH  Google Scholar 

  8. Pachpatte D.B.: Properties of solutions to nonlinear dynamic integral equations on time scales. Electron. J. Differ Equ. 2008(136), 1–8 (2008)

    Google Scholar 

  9. Pachpatte D.B.: On a nonlinear dynamic integrodifferential equations on time scales. J. Appl. Anal. 16, 279–294 (2010)

    Article  MathSciNet  Google Scholar 

  10. Tisdell C.C., Zaidi A.: Basic qualitative and quantitative results for solutions to nonlinear dynamic equations on time scales with an application to economic modelling. Nonlinear Anal. 68(11), 3504–3524 (2008)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Dr. B.A.M. University, Aurangabad, Maharashtra, 431004, India

    Deepak B. Pachpatte

Authors
  1. Deepak B. Pachpatte
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Deepak B. Pachpatte.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pachpatte, D.B. On Some Approximate Solutions of Nonlinear Integrodifferential Equation on Time Scales. Differ Equ Dyn Syst 20, 441–451 (2012). https://doi.org/10.1007/s12591-012-0141-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12591-012-0141-7

Keywords

Search

Navigation