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Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions. (English. Russian original) Zbl 1160.34301
The authors present interesting results on existence and uniqueness of fractional non-linear Cauchy-type problem involving the so-called Caputo Derivative.

34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
26A33Fractional derivatives and integrals (real functions)
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.
[2] Kilbas, A.A. and Trujillo, J.J., Applicable Analysis, 2001, vol. 78, no.1-2, pp. 153-192. · Zbl 1031.34002 · doi:10.1080/00036810108840931
[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. · doi:10.1090/S0002-9904-1938-06695-5
[4] Al-Bassam, M.A., J. Reine and Angew. Math., 1965, vol. 218, pp. 70-78. · Zbl 0156.30804 · doi:10.1515/crll.1965.218.70
[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.