Geodesic
The uniqueness of a~solution to the inverse Cauchy problem for a~fractional differential equation in a~Banach space
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2013), pp. 19-35

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We consider linear fractional differential operator equations involving Caputo derivative. The goal of this paper is to establish conditions of the unique solvability of the inverse Cauchy problem for these equations. We use properties of the Mittag-Leffler function and the calculus of sectorial operators in a Banach space. For equations with operators in a general form we obtain sufficient conditions for the unique solvability, and for equations with densely defined sectorial operators we obtain necessary and sufficient unique solvability conditions.
Keywords: fractional differential equations, Caputo derivative, Banach space, inverse Cauchy problem, uniqueness of solution, ill-posed problems, Mittag-Leffler function, calculus of sectorial operators
Mots-clés : fractional Fokker–Planck equation, subdiffusion. 
@article{IVM_2013_12_a2,
     author = {M. M. Kokurin},
     title = {The uniqueness of a~solution to the inverse {Cauchy} problem for a~fractional differential equation in {a~Banach} space},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {19--35},
     publisher = {mathdoc},
     number = {12},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_12_a2/}
}
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M. M. Kokurin. The uniqueness of a~solution to the inverse Cauchy problem for a~fractional differential equation in a~Banach space. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2013), pp. 19-35. http://geodesic.mathdoc.fr/item/IVM_2013_12_a2/