### Abstract

In this work, we investigate an inverse source problem for multi-term fractional mixed type equation in a rectangular domain. We seek solutions in a form of series expansions using orthogonal basis obtained by using the method of a separation of variables. The obtained solutions involve multi-variable Mittag-Leffler functions, and hence, certain properties of the multi-variable Mittag-Leffler function needed for our calculations were established and proved. Imposing certain conditions to the given data, the convergence of the infinite series solutions was proved as well.

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

Title of host publication | Trends in Mathematics |

Publisher | Springer International Publishing |

Pages | 289-301 |

Number of pages | 13 |

Edition | 9789811043369 |

DOIs | |

Publication status | Published - 2017 |

### Publication series

Name | Trends in Mathematics |
---|---|

Number | 9789811043369 |

ISSN (Print) | 2297-0215 |

ISSN (Electronic) | 2297-024X |

### Fingerprint

### Keywords

- Caputo operator
- Mittag-Leffler function
- Mixed type equation

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Trends in Mathematics*(9789811043369 ed., pp. 289-301). (Trends in Mathematics; No. 9789811043369). Springer International Publishing. https://doi.org/10.1007/978-981-10-4337-6_13

**Inverse source problem for multi-term fractional mixed type equation.** / Karimov, E. T.; Kerbal, S.; Al-Salti, N.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Trends in Mathematics.*9789811043369 edn, Trends in Mathematics, no. 9789811043369, Springer International Publishing, pp. 289-301. https://doi.org/10.1007/978-981-10-4337-6_13

}

TY - CHAP

T1 - Inverse source problem for multi-term fractional mixed type equation

AU - Karimov, E. T.

AU - Kerbal, S.

AU - Al-Salti, N.

PY - 2017

Y1 - 2017

N2 - In this work, we investigate an inverse source problem for multi-term fractional mixed type equation in a rectangular domain. We seek solutions in a form of series expansions using orthogonal basis obtained by using the method of a separation of variables. The obtained solutions involve multi-variable Mittag-Leffler functions, and hence, certain properties of the multi-variable Mittag-Leffler function needed for our calculations were established and proved. Imposing certain conditions to the given data, the convergence of the infinite series solutions was proved as well.

AB - In this work, we investigate an inverse source problem for multi-term fractional mixed type equation in a rectangular domain. We seek solutions in a form of series expansions using orthogonal basis obtained by using the method of a separation of variables. The obtained solutions involve multi-variable Mittag-Leffler functions, and hence, certain properties of the multi-variable Mittag-Leffler function needed for our calculations were established and proved. Imposing certain conditions to the given data, the convergence of the infinite series solutions was proved as well.

KW - Caputo operator

KW - Mittag-Leffler function

KW - Mixed type equation

UR - http://www.scopus.com/inward/record.url?scp=85030705141&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85030705141&partnerID=8YFLogxK

U2 - 10.1007/978-981-10-4337-6_13

DO - 10.1007/978-981-10-4337-6_13

M3 - Chapter

AN - SCOPUS:85030705141

T3 - Trends in Mathematics

SP - 289

EP - 301

BT - Trends in Mathematics

PB - Springer International Publishing

ER -