Geodesic
A uniqueness result for an inverse problem in a space-time fractional diffusion equation
Electronic journal of differential equations, Tome 2013 (2013)
Fractional (nonlocal) diffusion equations replace the integer-order derivatives in space and time by fractional-order derivatives. This article considers a nonlocal inverse problem and shows that the exponents of the fractional time and space derivatives are determined uniquely by the data $u(t, 0)= g(t),\; 0 t T$. The uniqueness result is a theoretical background for determining experimentally the order of many anomalous diffusion phenomena, which are important in physics and in environmental engineering.
Classification : 45K05, 35R30, 65M32
Keywords: fractional derivative, fractional Laplacian, weak solution, inverse problem, Mittag-Leffler function, Cauchy problem 
@article{EJDE_2013__2013__a83,
     author = {Tatar,  Salih and Ulusoy,  Suleyman},
     title = {A uniqueness result for an inverse problem in a space-time fractional diffusion equation},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1287.65076},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a83/}
}
TY  - JOUR
AU  - Tatar,  Salih
AU  - Ulusoy,  Suleyman
TI  - A uniqueness result for an inverse problem in a space-time fractional diffusion equation
JO  - Electronic journal of differential equations
PY  - 2013
VL  - 2013
UR  - http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a83/
LA  - en
ID  - EJDE_2013__2013__a83
ER  - 
%0 Journal Article
%A Tatar,  Salih
%A Ulusoy,  Suleyman
%T A uniqueness result for an inverse problem in a space-time fractional diffusion equation
%J Electronic journal of differential equations
%D 2013
%V 2013
%U http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a83/
%G en
%F EJDE_2013__2013__a83
Tatar,  Salih; Ulusoy,  Suleyman. A uniqueness result for an inverse problem in a space-time fractional diffusion equation. Electronic journal of differential equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a83/