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 Eurasian Math. J., 2016, Volume 7, Number 1, Pages 74–83 (Mi emj217)

Uniqueness of an inverse source non-local problem for fractional order mixed type equations

M. S. Salakhitdinov, E. T. Karimov

Department of Differential Equations, Institute of Mathematics, National University of Uzbekistan, 29 Durmon yuli St, 100125 Tashkent, Uzbekistan

Abstract: In the present work, we investigate the uniqueness of a solution to the inverse source problem with non-local conditions for a mixed parabolic-hyperbolic type equation with the Caputo fractional derivative. Solution of the problem we represent as bi-orthogonal series with respect to space variable and will get fractional order differential equations with respect to time-variable. Using boundary and gluing conditions, we deduce system of algebraic equations regarding unknown constants and imposing condition to the determinant of this system, we prove the uniqueness of the considered problem. Moreover, we find some non-trivial solutions to the problem in the case, in which the imposed conditions are not satisfie.

Keywords and phrases: inverse source problem, fractional order mixed type equation, Caputo fractional derivative.

 Funding Agency Grant Number Ministry of Education and Science of the Republic of Kazakhstan 3293/GF4 This work was partially supported by the Grant no. 3293/GF4 of the Ministry of Education and Science of the Republic of Kazakhstan.

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MSC: 35M10, 35R11, 35R30
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Citation: M. S. Salakhitdinov, E. T. Karimov, “Uniqueness of an inverse source non-local problem for fractional order mixed type equations”, Eurasian Math. J., 7:1 (2016), 74–83

Citation in format AMSBIB
\Bibitem{SalKar16} \by M.~S.~Salakhitdinov, E.~T.~Karimov \paper Uniqueness of an inverse source non-local problem for fractional order mixed type equations \jour Eurasian Math. J. \yr 2016 \vol 7 \issue 1 \pages 74--83 \mathnet{http://mi.mathnet.ru/emj217} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000380176800005} 

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This publication is cited in the following articles:
1. E. Karimov, N. Al-Salti, S. Kerbal, “An inverse source non-local problem for a mixed type equation with a Caputo fractional differential operator”, East Asian J. Appl. Math., 7:2 (2017), 417–438
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