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Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions. (English) 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.
MSC:
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
26A33Fractional derivatives and integrals (real functions)
References:
[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.