Advertisement

Differential Equations

, Volume 46, Issue 2, pp 208–213 | Cite as

Fractional differential equations with worsening right-hand sides

  • E. A. Barkova
  • P. P. Zabreiko
Partial Differential Equations
  • 59 Downloads

Abstract

We suggest methods for studying fractional differential equations with Caputo and Riemann-Liouville derivatives. Existence and uniqueness theorems are proved for the Cauchy problem for differential equations with worsening operators in scales of Banach spaces.

Keywords

Banach Space Cauchy Problem Uniqueness Theorem Lipschitz Condition Fractional Differential Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Zabreiko, P.P. and Radyno, Ya.V., Applications of Fixed Point Theory to the Cauchy Problem for Equations with Worsening Operators, Differ. Uravn., 1987, vol. 23, no. 2, pp. 345–348.MathSciNetGoogle Scholar
  2. 2.
    Zabreiko, P.P., Existence and Uniqueness Theorems for the Cauchy Problem for Differential Equations with Worsening Operators, Dokl. Akad. Nauk BSSR, 1989, vol. 23, no. 12, pp. 1061–1064.Google Scholar
  3. 3.
    Barkova, E.A. and Zabreiko, P.P., The Cauchy Problem for Higher-Order Differential Equations with Worsening Operators, Differ. Uravn., 1991, vol. 27, no. 3, pp. 472–478.MathSciNetGoogle Scholar
  4. 4.
    Barkova, E.A. and Zabreiko, P.P., The Cauchy Problem for Fractional Differential Equations with Worsening Right-Hand Sides, Differ. Uravn., 2006, vol. 42, no. 8, pp. 1132–1134.MathSciNetGoogle Scholar
  5. 5.
    Samko, S.G., Kilbas, A.A., and Marichev, O.I., Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya (Fractional Integrals and Derivatives with Some Applications), Minsk: Nauka i Tekhnika, 1987.zbMATHGoogle Scholar
  6. 6.
    Kilbas, A.A. and Trujillo, J.J., Differential Equations of Fractional Order: Methods, Results and Problems, Appl. Anal., 2001, vol. 1, no. 78, pp. 153–192.CrossRefMathSciNetGoogle Scholar
  7. 7.
    Fikhtengol’ts, G.M., Kurs differentsial’nogo i integral’nogo ischisleniya (Course of Differential and Integral Calculus), Moscow, 2003, vol. 2.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • E. A. Barkova
    • 1
    • 2
  • P. P. Zabreiko
    • 1
    • 2
  1. 1.Belarus State University of Computer Science and Radio ElectronicsMinskBelarus
  2. 2.Institute of MathematicsNational Academy of SciencesMinskBelarus

Personalised recommendations