ON SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR THE POISSON EQUATION WITH A NONLOCAL BOUNDARY OPERATOR

doi:10.1016/S0252-9602(15)30031-X

Abstract

Abstract:

In this work, we investigate the solvability of the boundary value problem for the Poisson equation, involving a generalized Riemann-Liouville and the Caputo derivative of fractional order in the class of smooth functions. The considered problems are generalization of the known Dirichlet and Neumann problems with operators of a fractional order.

Key words: operator of fractional integration and differentiation, solvability, boundary value problem, Riemann-Liouville operator, Caputo fractional derivative, Poisson equation, Dirichlet and Neumann problems

CLC Number:

35J05

B. J. KADIRKULOV, M. KIRANE. ON SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR THE POISSON EQUATION WITH A NONLOCAL BOUNDARY OPERATOR[J].Acta mathematica scientia,Series B, 2015, 35(5): 970-980.

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