Geodesic
Parameter determination in a differential equation of fractional order with Riemann--Liouville fractional derivative in a Hilbert space
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 8 (2015) no. 1, pp. 55-63

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The Cauchy type problem for a differential equation with fractional derivative and self-adjoint operator in a Hilbert space is considered. The problem of parameter determination in equation by the value of the solution at a fixed point is presented. Theorems of existence and uniqueness of the solution are proved.
Keywords: equation of fractional order, Hilbert space, self-adjoint operator, Cauchy-type problem, Mittag–Leffler function, inverse problem, characteristic function. 
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     author = {Dmitry G. Orlovsky},
     title = {Parameter determination in a differential equation of fractional order with {Riemann--Liouville} fractional derivative in a {Hilbert} space},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {55--63},
     publisher = {mathdoc},
     volume = {8},
     number = {1},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2015_8_1_a7/}
}
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Dmitry G. Orlovsky. Parameter determination in a differential equation of fractional order with Riemann--Liouville fractional derivative in a Hilbert space. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 8 (2015) no. 1, pp. 55-63. http://geodesic.mathdoc.fr/item/JSFU_2015_8_1_a7/