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


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.


Fundamental Solution Fractional Derivative Regular Solution Fractional Calculus Rectangular Domain 
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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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