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On perturbations of abstract fractional differential equations by nonlinear operators

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Abstract

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.

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Correspondence to A. V. Glushak.

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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 35, Proceedings of the Fifth International Conference on Differential and Functional Differential Equations. Part 1, 2010.

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Avad, H.K., Glushak, A.V. On perturbations of abstract fractional differential equations by nonlinear operators. J Math Sci 170, 306–323 (2010). https://doi.org/10.1007/s10958-010-0087-7

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