Electron. J. Diff. Equ., Vol. 2016 (2016), No. 14, pp. 1-9.

Inverse problems of periodic spatial distributions for a time fractional diffusion equation

Halyna Lopushanska, Andrzej Lopushansky, Olga Myaus

For a time fractional diffusion equation and a diffusion-wave equation with Caputo partial derivative we prove the inverse problem is well posed. This problem consists in the restoration of the initial data of a classical solution in time and with values in a space of periodic spatial distributions. A time integral over-determination condition is used.

Submitted November 25, 2015. Published January 7, 2016.
Math Subject Classifications: 35S15.
Key Words: Fractional derivative; inverse problem; integral at times; over-determination.

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Halyna Lopushanska
Department of Differential Equations
Ivan Franko National University of Lviv, Ukraine
email: lhp@ukr.net
  Andrzej Lopushansky
Rzeszów University, Rejtana str., 16A
35-310 Rzeszóow, Poland
email: alopushanskyj@gmail.com
  Olga Myaus
Department of Higher Mathematics
National University "Lviv Polytechnic", Ukraine
email: myausolya@mail.ru

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