Mathematical Notes

, Volume 77, Issue 1, pp 26–38

Cauchy-type problem for an abstract differential equation with fractional derivatives

  • A. V. Glushak
Article

DOI: 10.1007/s11006-005-0003-5

Cite this article as:
Glushak, A.V. Math Notes (2005) 77: 26. doi:10.1007/s11006-005-0003-5

Abstract

The uniform well-posedness of a Cauchy-type problem with two fractional derivatives and bounded operator A is proved. For an unbounded operator A we present a test for the uniform well-posedness of the problem under consideration consistent with the test for the uniform well-posedness of the Cauchy problem for an equation of second order.

Key words

Cauchy-type problemdifferential equation with fractional derivativesuniform well-posednessBanach spaceMellin integralPost-Widder inversion formula

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • A. V. Glushak
    • 1
  1. 1.Voronezh State Technical UniversityRussia