TY - JOUR
T1 - Direct and inverse problems for a Samarskii-Ionkin type problem for a two dimensional fractional parabolic equation
AU - Kerbal, Sebti
AU - Kadirkulov, Bakhtiyar Jalilovich
AU - Kirane, Mokhtar
N1 - Publisher Copyright:
© 2018 NSP.
PY - 2018/7/1
Y1 - 2018/7/1
N2 - Samarskii-Ionkin type problems are known classes of problems that represent a generalization of classical ones. At the same time they are obtained in a natural way by constructing mathematical models of real processes and phenomena in physics, engineering, sociology, ecology, etc. Here we investigate the ability to solve non-local problems of its type in 2D using the Fourier method of the separation of variables. We study the completeness of the root functions of the corresponding spectral problems in L2(0 < x, y < 1), when they are defined as products of two systems of functions, where one of them is an orthonormal basis, and another is a Riesz basis. Using the properties of biorthogonal systems, we also study the problem of identifying the source function in the spatial domain.
AB - Samarskii-Ionkin type problems are known classes of problems that represent a generalization of classical ones. At the same time they are obtained in a natural way by constructing mathematical models of real processes and phenomena in physics, engineering, sociology, ecology, etc. Here we investigate the ability to solve non-local problems of its type in 2D using the Fourier method of the separation of variables. We study the completeness of the root functions of the corresponding spectral problems in L2(0 < x, y < 1), when they are defined as products of two systems of functions, where one of them is an orthonormal basis, and another is a Riesz basis. Using the properties of biorthogonal systems, we also study the problem of identifying the source function in the spatial domain.
KW - Bi-orthonormal system
KW - Eigenfunctions
KW - Eigenvalues
KW - Fractional differential operator
KW - Non-local problems
KW - Riesz basis
KW - Root functions
KW - Samarskii-Ionkin type problem
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U2 - 10.18576/pfda/040301
DO - 10.18576/pfda/040301
M3 - Article
AN - SCOPUS:85051781394
SN - 2356-9336
VL - 4
SP - 147
EP - 160
JO - Progress in Fractional Differentiation and Applications
JF - Progress in Fractional Differentiation and Applications
IS - 3
ER -