### Abstract

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 L^{2}(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.

Original language | English |
---|---|

Pages (from-to) | 147-160 |

Number of pages | 14 |

Journal | Progress in Fractional Differentiation and Applications |

Volume | 4 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jul 1 2018 |

### Fingerprint

### Keywords

- Bi-orthonormal system
- Eigenfunctions
- Eigenvalues
- Fractional differential operator
- Non-local problems
- Riesz basis
- Root functions
- Samarskii-Ionkin type problem

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Progress in Fractional Differentiation and Applications*,

*4*(3), 147-160. https://doi.org/10.18576/pfda/040301

**Direct and inverse problems for a Samarskii-Ionkin type problem for a two dimensional fractional parabolic equation.** / Kerbal, Sebti; Kadirkulov, Bakhtiyar Jalilovich; Kirane, Mokhtar.

Research output: Contribution to journal › Article

*Progress in Fractional Differentiation and Applications*, vol. 4, no. 3, pp. 147-160. https://doi.org/10.18576/pfda/040301

}

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

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

UR - http://www.scopus.com/inward/record.url?scp=85051781394&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85051781394&partnerID=8YFLogxK

U2 - 10.18576/pfda/040301

DO - 10.18576/pfda/040301

M3 - Article

VL - 4

SP - 147

EP - 160

JO - Progress in Fractional Differentiation and Applications

JF - Progress in Fractional Differentiation and Applications

SN - 2356-9336

IS - 3

ER -