Skip to main content
SpringerLink
Log in

Modified cauchy problem for a loaded second-order parabolic equation with constant coefficients

  • Partial Differential Equations
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We give a well-posed statement of the initial value problem for a second-order parabolic equation containing Riemann–Liouville fractional partial derivatives in one of the two independent variables. We prove existence and uniqueness theorems for the solution of this problem.

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. Nakhushev, A.M., Drobnoe ischislenie i ego primenenie (Fractional Calculus and Its Application), Moscow, 2003.

    Google Scholar 

  2. Pskhu, A.V., Uravneniya v chastnykh proizvodnykh drobnogo poryadka (Fractional Partial Differential Equations), Moscow: Nauka, 2005.

    MATH  Google Scholar 

  3. Kochubei, A.N., Cauchy Problem for Fractional Diffusion-Wave Equations with Variable Coefficients, Appl. Anal., 2014, vol. 93, no. 10, pp. 2211–2242.

    Article  MATH  MathSciNet  Google Scholar 

  4. Mamchuev, M.O., General Representation of the Solution of a Fractional Diffusion Equation with Constant Coefficients in a Rectangular Domain, Izv. Kabardino-Balkar. Nauch. Tsentra RAN, 2004, no. 2 (12), pp. 116–118.

    Google Scholar 

  5. Mamchuev, M.O., Boundary Value Problems for a Fractional Diffusion Equation with Constant Coefficients, Dokl. Adyg. (Cherkess) Mezhdunar. Akad. Nauk, 2005, vol. 7, no. 2, pp. 38–45.

    Google Scholar 

  6. Orsinger, E. and Beghin, L., Time-Fractional Telegraph Equations and Telegraph Processes with Brownian Time, Probab. Theory Related Fields, 2004, vol. 128, no. 1, pp. 141–160.

    Article  MathSciNet  Google Scholar 

  7. Huang, F., Analytic Solution of the Time-Fractional Telegraph Equation, J. Appl. Math., 2009, vol. 2009, Article ID890158, 9 pages.

  8. Chen, J., Liu, F., and Anh, V., Analytical Solution for the Time-Fractional Telegraph Equation by the Method of Separating Variables, J. Math. Anal. Appl., 2008, vol. 338, no. 2, pp. 1364–1377.

    Article  MATH  MathSciNet  Google Scholar 

  9. Mamchuev, M.O., Fundamental Solution of a Second-Order Loaded Parabolic Equation with Constant Coefficients, Differ. Uravn., 2015, vol. 51, no. 5, pp. 611–620.

    Google Scholar 

  10. Mamchuev, M.O., Fundamental Solution of a System of Fractional Partial Differential Equations, Differ. Uravn., 2010, vol. 46, no. 8, pp. 1113–1124.

    MathSciNet  Google Scholar 

  11. Mamchuev, M.O., Cauchy Problem in Nonlocal Statement for a System of Fractional Partial Differential Equations, Differ. Uravn., 2012, vol. 48, no. 3, pp. 351–358.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Applied Mathematics and Automation, Nalchik, Russia

    M. O. Mamchuev

Authors
  1. M. O. Mamchuev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. O. Mamchuev.

Additional information

Original Russian Text © M.O. Mamchuev, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 9, pp. 1147–1153.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mamchuev, M.O. Modified cauchy problem for a loaded second-order parabolic equation with constant coefficients. Diff Equat 51, 1137–1144 (2015). https://doi.org/10.1134/S0012266115090037

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266115090037

Keywords

Search

Navigation