### 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 |
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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 |

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### 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