Geodesic
On perturbations of abstract fractional differential equations by nonlinear operators
Contemporary Mathematics. Fundamental Directions, Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17–24, 2008). Part 1, Tome 35 (2010), pp. 5-21

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We prove the unique solvability of a Cauchy-type problem for an abstract parabolic equation containing fractional derivatives and a nonlinear perturbation term. The result is applied to establish the solvability of the inverse coefficient problem for a fractional-order equation. 
@article{CMFD_2010_35_a0,
     author = {H. K. Avad and A. V. Glushak},
     title = {On perturbations of abstract fractional differential equations by nonlinear operators},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {5--21},
     publisher = {mathdoc},
     volume = {35},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2010_35_a0/}
}
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H. K. Avad; A. V. Glushak. On perturbations of abstract fractional differential equations by nonlinear operators. Contemporary Mathematics. Fundamental Directions, Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17–24, 2008). Part 1, Tome 35 (2010), pp. 5-21. http://geodesic.mathdoc.fr/item/CMFD_2010_35_a0/