Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions. (English. Russian original) Zbl 1160.34301

Differ. Equ. 41, No. 1, 84-89 (2005); translation from Differ. Uravn. 41, No. 1, 82-86 (2005).
The authors present interesting results on existence and uniqueness of fractional non-linear Cauchy-type problem involving the so-called Caputo Derivative.


34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
26A33 Fractional derivatives and integrals
Full Text: DOI


[1] Samko, S.G., Kilbas, A.A., and Marichev, O.I., Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya (Fractional Integrals and Derivatives and Some of Their Applications), Minsk, 1987. · Zbl 0617.26004
[2] Kilbas, A.A. and Trujillo, J.J., Applicable Analysis, 2001, vol. 78, no.1-2, pp. 153-192. · Zbl 1031.34002
[3] Pitcher, E. and Sewell, W.E., Bull. Amer. Math. Soc., 1938, vol. 44, no.2, pp. 100-107; Errata // Ibid, no. 12, p. 888. · Zbl 0018.30701
[4] Al-Bassam, M.A., J. Reine and Angew. Math., 1965, vol. 218, pp. 70-78. · Zbl 0156.30804
[5] Leskovskii, I.P., Differents. Uravn., 1977, vol. 13, no.1, pp. 170-173.
[6] Semenchuk, N.P., Differents. Uravn., 1982, vol. 18, no.10, pp. 1831-1833.
[7] Kilbas, A.A., Bonilla, B., and Trujillo, J.J., Dokl. Akad. Nauk Belarusi, 2000, vol. 44, no.6, pp. 18-22.
[8] Kilbas, A.A., Bonilla, B., and Trujillo, J.J., Demonstratio Math., 2000, vol. 33, no.3, pp. 583-602.
[9] Kilbas, A.A. and Marzan, S.A., Dokl. NAN Belarusi, 2003, vol. 47, no.1, pp. 29-35.
[10] Kolmogorov, A.N. and Fomin, S.V., Elementy teorii funktsii i funktsional?nogo analiza (Elements of Function Theory and Functional Analysis), Moscow, 1981.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.