On the compactness and the uniform continuity of a resolvent family for a fractional differential equation

Authors

  • А.V. Antoniouk
  • А.N. Kochubei
  • S. I. Piskarev

DOI:

https://doi.org/10.15407/dopovidi2014.06.007

Keywords:

compactness, continuity, fractional differential equation

Abstract

The compactness and the uniform continuity for a resolvent family of operators for fractional differential equations in a Banach space are studied.

Downloads

References

Pazy A. Semigroups of linear operators and applications to partial differential equations. New York: Springer, 1983. https://doi.org/10.1007/978-1-4612-5561-1

Cuthbert J. R. Z. Wahrsch. und Verw. Geb., 1971, 18, No. 1–2: 9–16. https://doi.org/10.1007/BF00538484

Engel K.-J., Nagel R. One-parameter semigroups for linear evolution equations. Berlin: Springer, 2000.

Bobylev N. A., Kim J. K., Korovin S. K., Piskarev S. Nonlinear Anal., 1998, 33, No. 5: 473–482. https://doi.org/10.1016/S0362-546X(97)00560-9

Piskarev S. Mat. Zam., 1988, 44, No. 1: 112–123.

Prüss J. Evolutionary integral equation and applications. Basel: Birkhäuser, 1993. https://doi.org/10.1007/978-3-0348-8570-6

Kilbas A. A., Srivastava H. M., Trujillo J. J. Theory and applications of fractional differential equations. Amsterdam: Elsevier, 2006..

Chen Ch., Li M. Semigroup Forum, 2010, 80: 121–142. https://doi.org/10.1007/s00233-009-9184-7

Peng J., Li K. J. Math. Anal. Appl., 2012, 385: 786–796. https://doi.org/10.1016/j.jmaa.2011.07.009

Kochubei A. N. Different. Equat., 1989, 25: 967–974.

Bazhlekova E. Fract. Calc. Appl. Anal., 1998, 1: 255–270.

Bazhlekova E. Fract. Calc. Appl. Anal., 2000, 3: 213–230.

Arendt W., Batty C. J. K., Hieber M., Neubrander F. Vector-valued Laplace transforms and Cauchy problems. Basel: Birkhäuser, 2011. https://doi.org/10.1007/978-3-0348-0087-7

Voigt J. Note Mat., 1992, 12: 259–269.

Lizama C. Proc. Amer. Math. Soc., 1998, 126: 3581–3587. https://doi.org/10.1090/S0002-9939-98-04594-8

Downloads

Published

26.02.2025

How to Cite

Antoniouk А., Kochubei А., & Piskarev, S. I. (2025). On the compactness and the uniform continuity of a resolvent family for a fractional differential equation . Reports of the National Academy of Sciences of Ukraine, (6), 7–12. https://doi.org/10.15407/dopovidi2014.06.007

Issue

No. 6 (2014): Reports of the National Academy of Sciences of Ukraine

Section

Mathematics

License

Copyright (c) 2025 Reports of the National Academy of Sciences of Ukraine

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.