Geodesic
On the Properties of a Cauchy-Type Problem for an Abstract Differential Equation with Fractional Derivatives
Matematičeskie zametki, Tome 82 (2007) no. 5, pp. 665-677

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We study the relationship between the solutions of abstract differential equations with fractional derivatives and their stability with respect to the perturbation by a bounded operator. Besides, we obtain representations for the solution of an inhomogeneous equation and for an equation containing a fractional power of the generator of a cosine operator function.
Keywords: differential equation with fractional derivatives, Cauchy-type problem, Riemann–Liouville fractional derivative, fractional integral, Mittag-Leffler function. 
@article{MZM_2007_82_5_a2,
     author = {A. V. Glushak},
     title = {On the {Properties} of a {Cauchy-Type} {Problem} for an {Abstract} {Differential} {Equation} with {Fractional} {Derivatives}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {665--677},
     publisher = {mathdoc},
     volume = {82},
     number = {5},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_5_a2/}
}
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A. V. Glushak. On the Properties of a Cauchy-Type Problem for an Abstract Differential Equation with Fractional Derivatives. Matematičeskie zametki, Tome 82 (2007) no. 5, pp. 665-677. http://geodesic.mathdoc.fr/item/MZM_2007_82_5_a2/