### Abstract

In the present work, we have considered a non-local boundary problem with integral matching conditions for mixed type equation,involving fractional diffusion and wave equations. Using specific algorithm we find solution of considered problem in an explicit form. The proof is based on the method of characteristics, Green's function, Voltera integral equations and solution of a second order ordinary differential equation.

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

Pages (from-to) | 95-104 |

Number of pages | 10 |

Journal | Mathematical Modelling of Natural Phenomena |

Volume | 12 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2017 |

### Fingerprint

### Keywords

- Caputo derivative
- Integral form transmitting condition
- Mixed type equation

### ASJC Scopus subject areas

- Modelling and Simulation

### Cite this

*Mathematical Modelling of Natural Phenomena*,

*12*(3), 95-104. https://doi.org/10.1051/mmnp/201712309

**Non-local Boundary Problem with Integral Form Transmitting Condition for Fractional Mixed Type Equation in a Composite Domain.** / Kerbal, S.; Karimov, E.; Rakhmatullaeva, N.

Research output: Contribution to journal › Article

*Mathematical Modelling of Natural Phenomena*, vol. 12, no. 3, pp. 95-104. https://doi.org/10.1051/mmnp/201712309

}

TY - JOUR

T1 - Non-local Boundary Problem with Integral Form Transmitting Condition for Fractional Mixed Type Equation in a Composite Domain

AU - Kerbal, S.

AU - Karimov, E.

AU - Rakhmatullaeva, N.

PY - 2017

Y1 - 2017

N2 - In the present work, we have considered a non-local boundary problem with integral matching conditions for mixed type equation,involving fractional diffusion and wave equations. Using specific algorithm we find solution of considered problem in an explicit form. The proof is based on the method of characteristics, Green's function, Voltera integral equations and solution of a second order ordinary differential equation.

AB - In the present work, we have considered a non-local boundary problem with integral matching conditions for mixed type equation,involving fractional diffusion and wave equations. Using specific algorithm we find solution of considered problem in an explicit form. The proof is based on the method of characteristics, Green's function, Voltera integral equations and solution of a second order ordinary differential equation.

KW - Caputo derivative

KW - Integral form transmitting condition

KW - Mixed type equation

UR - http://www.scopus.com/inward/record.url?scp=85019985956&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85019985956&partnerID=8YFLogxK

U2 - 10.1051/mmnp/201712309

DO - 10.1051/mmnp/201712309

M3 - Article

VL - 12

SP - 95

EP - 104

JO - Mathematical Modelling of Natural Phenomena

JF - Mathematical Modelling of Natural Phenomena

SN - 0973-5348

IS - 3

ER -