### 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 |
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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 |
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Number | 9789811043369 |

ISSN (Print) | 2297-0215 |

ISSN (Electronic) | 2297-024X |

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Karimov, E. T., Kerbal, S., & Al-Salti, N. (2017). Inverse source problem for multi-term fractional mixed type equation. In

*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