Skip to main content
SpringerLink
Log in

The Weighted Cauchy Type Problem and Cauchy Problem for the Linear Barbashin Integro-Differential Equations with Fractional Partial Derivative

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

We establish the existence and uniqueness conditions for the weighted Cauchy type problem and the Cauchy problem for the linear Barbashin integro-differential equation with fractional partial derivative of order 0 < α ≤ 1 in the sense of Riemann–Liouville and Caputo. Bibliography: 8 titles.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. J. M. Appell, A. S. Kalitvin, and P. P. Zabrejko, Partial Integral Operators and Integro-Differential Equations, Marcel Dekker, New York (2000).

    MATH  Google Scholar 

  2. A. S. Kalitvin, Linear Operators with Partial Integrals [in Russian], Voronezh (2000).

  3. A. S. Kalitvin and V. A. Kalitvin, The Volterra and Volterra-Fredholm Integral Equations with Partial Integrals [in Russian], Lipetsk State Pedag. Univ. Press, Lipetsk (2006).

  4. A. S. Kalitvin and E. V. Frolova, Linear Equations with Partial Integrals. C-Theory [in Russian], Lipetsk State Pedag. Univ. Press, Lipetsk (2004).

  5. A. S. Kalitvin, “Spectral properties of partial integral operators of Volterra and Volterra-Fredholm type,” Z. Anal. Anwend. 17, No. 2, 297-309 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  6. A. S. Kalitvin, “On Volterra operators and equations with partial integrals,” In: S. G. Krein Voronezh Winter Mathematical School-2012, pp. 91-94, Voronezh State Univ. Press, Voronezh (2012).

  7. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Integrals and Fractional Order Derivatives and Applications [in Russian], Nauka Tekhnika, Minsk (1987).

  8. A. A. Kilbas, M. M. Srivastava, and J. J. Trujllo, Theory and Applications of Fractional Differential Equations, Elsevier, New York etc. (2006).

Download references

Author information

Authors and Affiliations

  1. Lipetsk State Pedagogical University, 42, Lenina St., Lipetsk, 398020, Russia

    A. S. Kalitvin & V. A. Kalitvin

Authors
  1. A. S. Kalitvin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. A. Kalitvin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. S. Kalitvin.

Additional information

Translated from Problemy Matematicheskogo Analiza 85, June 2016, pp. 119-125.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kalitvin, A.S., Kalitvin, V.A. The Weighted Cauchy Type Problem and Cauchy Problem for the Linear Barbashin Integro-Differential Equations with Fractional Partial Derivative. J Math Sci 219, 125–132 (2016). https://doi.org/10.1007/s10958-016-3088-3

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-016-3088-3

Search

Navigation