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

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.

Identifiers

DOI

10.1134/s0012266115050055

Citations and references