Electron. J. Differential Equations, Vol. 2017 (2017), No. 182, pp. 1-14.

Inverse source Cauchy problem for a time fractional diffusion-wave equation with distributions

Andrzej Lopushansky, Halyna Lopushansk

Abstract:
We study the inverse Cauchy problem for a time fractional diffusion-wave equation with distributions in right-hand sides. The problem is to find a solution (continuous in time in generalized sense) of the direct problem and an unknown continuous time-dependent part of a source. The unique solvability of the problem is established.

Submitted April 24, 2017. Published July 18, 2017.
Math Subject Classifications: 35S15.
Key Words: Distribution; fractional derivative; inverse problem; Green vector-function.

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  Andrzej Lopushansky
Rzeszów University
Rejtana str., 16A, 35-310 Rzeszów, Poland
email: alopushanskyj@gmail.com
Halyna Lopushanska
Department of Differential Equations
Ivan Franko National University of Lviv, Ukraine
email: lhp@ukr.net

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