Article

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

Abdumauvlen BerdyshevKazakh National Pedagogical University named after Abai , Almaty, Zhubanov str. 1 , 050010 , KazakhstanB. J. KadirkulovTashkent State Institute for Oriental Studies , Tashkent , UzbekistanJuan J. NietoInstitute of Mathematics , University of Santiago de Compostela , Santiago de Compostela , Spain ; Department of Mathematics , Faculty of Science, King Abdulaziz University , P.O.Box 80203, Jeddah , 21589 , Saudi Arabia

Complex Variables and Elliptic Equationsjournal2013en

ABI

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.

Topics

Differential Equations and Boundary Problems Differential Equations and Numerical Methods Fractional Differential Equations Solutions

Identifiers

DOI: 10.1080/17476933.2013.777711

Citations and references

Cited by 3 16 references

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