Mathematical Notes

, Volume 82, Issue 5, pp 596–607

On the properties of a Cauchy-type problem for an abstract differential equation with fractional derivatives

Article

DOI: 10.1134/S000143460711003X

Cite this article as:
Glushak, A.V. Math Notes (2007) 82: 596. doi:10.1134/S000143460711003X

Abstract

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.

Key words

differential equation with fractional derivatives Cauchy-type problem Riemann-Liouville fractional derivative fractional integral Mittag-Leffler function 

Copyright information

© Pleiades Publishing, Ltd. 2007

Authors and Affiliations

  1. 1.Belgorod State UniversityRussia