Mathematical Notes

, Volume 77, Issue 1, pp 26–38

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


  • A. V. Glushak
    • Voronezh State Technical University

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


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
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© Springer Science+Business Media, Inc. 2005