This article is cited in 1 scientific paper (total in 1 paper)
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
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.
PDF file (332 kB)
MSC: 35M10, 35R11, 35R30
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
\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.
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This publication is cited in the following articles:
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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