Geodesic
On the solvability of an abstract differential equation of fractional order with a~variable operator
Contemporary Mathematics. Fundamental Directions, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 3, Tome 47 (2013), pp. 18-32

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One-valued solvability of initial problems for differential equations of fractional order with a variable operator is obtained by the Tanabe–Sobolevskii method modified in conformity with fractional-order equations in a Banach space. 
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     title = {On the solvability of an abstract differential equation of fractional order with a~variable operator},
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A. V. Glushak; H. K. Avad. On the solvability of an abstract differential equation of fractional order with a~variable operator. Contemporary Mathematics. Fundamental Directions, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 3, Tome 47 (2013), pp. 18-32. http://geodesic.mathdoc.fr/item/CMFD_2013_47_a1/