Geodesic
Uniqueness of an inverse source non-local problem for fractional order mixed type equations
Eurasian mathematical journal, Tome 7 (2016) no. 1, pp. 74-83.

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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. 
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M. S. Salakhitdinov; E. T. Karimov. Uniqueness of an inverse source non-local problem for fractional order mixed type equations. Eurasian mathematical journal, Tome 7 (2016) no. 1, pp. 74-83. http://geodesic.mathdoc.fr/item/EMJ_2016_7_1_a5/

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