Geodesic
Inverse problems for evolution equations with fractional integrals at boundary-value conditions
Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 29 (2008), pp. 49-61

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The following problem is considered: to find a solution and a term of a first-order differential equation in a Banach space if the initial-value condition and an excessive condition containing the fractional Riemann–Liouville integral are given. We show that the solvability of the considered problem depends on the distributions of zeroes of the Mittag-Leffler function. 
@article{CMFD_2008_29_a3,
     author = {A. V. Glushak},
     title = {Inverse problems for evolution equations with fractional integrals at boundary-value conditions},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {49--61},
     publisher = {mathdoc},
     volume = {29},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2008_29_a3/}
}
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A. V. Glushak. Inverse problems for evolution equations with fractional integrals at boundary-value conditions. Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 29 (2008), pp. 49-61. http://geodesic.mathdoc.fr/item/CMFD_2008_29_a3/