Timurkhan S. Aleroev, Mokhtar Kirane, Salman A. Malik
Abstract:
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 |
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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 |
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Salman A. Malik Department of Mathematics COMSATS Institute of Information Technology Islamabad, Pakistan email: salman.amin.malik@gmail.com |
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