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Differential Equations

, Volume 51, Issue 5, pp 620–629 | Cite as

Fundamental solution of a loaded second-order parabolic equation with constant coefficients

  • M. O. MamchuevEmail author
Partial Differential Equations

Abstract

We study a second-order partial differential equation containing fractional derivatives with respect to one of the two independent variables. We construct a fundamental solution of this equation, analyze its properties, and derive a general representation of solutions in a rectangular domain. It follows from this representation that the presence of a lower fractional derivative in the equation may affect the well-posedness of initial and initial–boundary value problems.

Keywords

Fundamental Solution Fractional Derivative Regular Solution Fractional Calculus Rectangular Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Institute for Applied Mathematics and Automation, Kabardino-Balkar Scientific CenterRussian Academy of SciencesNal’chikRussia

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