Growth of solutions of fractional differential equations

TitleGrowth of solutions of fractional differential equations
Publication TypeJournal Article
Year of Publication2016
AuthorsSemochko, NS, Chyzhykov, IE
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2016.08.012
Issue8
SectionMathematics
Pagination12-18
Date Published8/2016
LanguageUkrainian
Abstract

We prove the existence and uniqueness of a solution of some fractional differential equation. With the aid of the Wiman–Valiron method, the order of growth for the solution is found as well.

Keywordsdifferential equation, entire function, fractional derivative, Wiman–Valiron method
References: 
  1. Kilbas A. A., Rivero M., Rodriguez-Germá L., Trujillo J. J. Appl. Math. Comput., 2007, 187: 239–249. https://doi.org/10.1016/j.amc.2006.08.121
  2. Kilbas A. A., Srivastava H. M., Trujillo J. J. Theory and Applications of Fractional Differential Equations, Amsterdam: Elsevier, 2006.
  3. Kochubei A. N. Fract. Calc. Appl. Anal., 2009, 12, No 2: 135–158.
  4. Wittich H. Neuere Untersuchungen über eindeutige analytische Funktionen, 2nd ed., Berlin: Springer, 1968. https://doi.org/10.1007/978-3-642-87594-6
  5. Chyzhykov I., Gundersen G. G., Heittokangas J. Proc. London Math. Soc., 2003, 86, Iss. 3: 735–754. https://doi.org/10.1112/S0024611502013965
  6. Laine I. Nevanlinna Theory and Complex Differential Equations, Berlin: Walter de Gruyter, 1993. https://doi.org/10.1515/9783110863147
  7. Samko S. G., Kilbas A. A., Marichev O. I. Fractional Integrals and Derivatives: Theory and Applications, New York: Gordon and Brach, 1993.
  8. Djrbashian M. M. Integral transformations and representations of functions in a complex domain, Moscow: Nauka, 1966 (in Russian).
  9. Sheremeta M. M. Analytic functions of bounded l-index, Mathematical Studies: Monograph Series, Vol. 6, Lviv: VNTL, 1999.
  10. Hayman W. K. Canad. Math. Bull., 1974, 17, No 3: 317–358. https://doi.org/10.4153/CMB-1974-064-0
  11. Chyzhykov I. E., Semochko N.S. Int. J. Appl. Math., 2016, 29, No 1: 19–30. https://doi.org/10.12732/ijam.v29i1.3