Geodesic
A uniqueness result for an inverse problem in a space-time fractional diffusion equation
Electronic Journal of Differential Equations, Tome 2013 (2013).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     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},
     publisher = {mathdoc},
     volume = {2013},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a183/}
}
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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__a183/