Solvability of an elliptic partial differential equation with boundary condition involving fractional derivatives

2013

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DOI 10.1080/17476933.2013.777711
Data confidence 70 medium
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Abstract

We study an elliptic equation in a regular domain with a condition on the boundary involving a generalized Riemann–Liouville derivative of fractional order. The Bitsadze-Samarskii type problem is formulated for that equation. The uniqueness is proved by the maximum principle for harmonic functions. The Poisson kernel of the Dirichlet problem for the Laplace equation is used for proving the existence of a solution for the formulated problem.