Geodesic
Determination of a source term for a time fractional diffusion equation with an integral type over-determining condition
Electronic journal of differential equations, Tome 2013 (2013)
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.
Classification : 80A23, 65N21, 26A33, 45J05, 34K37, 42A16
Keywords: inverse problem, heat equation, fractional derivative, integral equations, bi-orthogonal system of functions, Fourier series 
@article{EJDE_2013__2013__a165,
     author = {Aleroev,  Timurkhan S. and Kirane,  Mokhtar and Malik,  Salman A.},
     title = {Determination of a source term for a time fractional diffusion equation with an integral type over-determining condition},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1288.80012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a165/}
}
TY  - JOUR
AU  - Aleroev,  Timurkhan S.
AU  - Kirane,  Mokhtar
AU  - Malik,  Salman A.
TI  - Determination of a source term for a time fractional diffusion equation with an integral type over-determining condition
JO  - Electronic journal of differential equations
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VL  - 2013
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LA  - en
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%A Kirane,  Mokhtar
%A Malik,  Salman A.
%T Determination of a source term for a time fractional diffusion equation with an integral type over-determining condition
%J Electronic journal of differential equations
%D 2013
%V 2013
%U http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a165/
%G en
%F EJDE_2013__2013__a165
Aleroev,  Timurkhan S.; Kirane,  Mokhtar; Malik,  Salman A. Determination of a source term for a time fractional diffusion equation with an integral type over-determining condition. Electronic journal of differential equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a165/