Electron. J. Diff. Equ., Vol. 2013 (2013), No. 270, pp. 1-16.

Determination of a source term for a time fractional diffusion equation with an integral type over-determining condition

Timurkhan S. Aleroev, Mokhtar Kirane, Salman A. Malik

We consider a linear heat equation involving a fractional derivative in time, with a nonlocal boundary condition. We determine a source term independent of the space variable, and the temperature distribution for a problem with an over-determining condition of integral type. We prove the existence and uniqueness of the solution, and its continuous dependence on the data.

Submitted November 1, 2013. Published December 6, 2013.
Math Subject Classifications: 80A23, 65N21, 26A33, 45J05, 34K37, 42A16.
Key Words: Inverse problem; heat equation; fractional derivative; integral equations; bi-orthogonal system of functions; Fourier series.

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Timurkhan S. Aleroev
The State University of the Ministry of Finance
of the Russian Federation, Moscow.
Moscow State Academy of Municipal Services and Construction
Moscow, Russia
email: aleroev@mail.ru
Mokhtar Kirane
Laboratoire de Mathématiques, Image et Applications
Université de La Rochelle
Avenue M. Crépeau, 17042 La Rochelle Cedex, France
email: mokhtar.kirane@univ-lr.fr
Salman A. Malik
Department of Mathematics
COMSATS Institute of Information Technology
Islamabad, Pakistan
email: salman.amin.malik@gmail.com

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