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Generalized quasilinearization for fractional differential equations. (English) Zbl 1189.34010
Summary: An existence and uniqueness result is obtained for an IVP of fractional differential equations using the method of generalized quasilinearization, which allows for some relaxation on the conditions on f.
34A08Fractional differential equations
26A33Fractional derivatives and integrals (real functions)
45J05Integro-ordinary differential equations
[1]Lakshmikantham, V.; Vatsala, A. S.: Generalized quasilinearization for nonlinear problems, (1998)
[2]Devi, J. Vasundhara; Suseela, Ch.: Quasilinearization for fractional differential equations, Communications in applied analysis 12, No. 4, 407-418 (2008) · Zbl 1184.34015
[3]Deekshitulu, G. V. S.R.: Generalized monotone iterative technique for fractional R–L differential equations, Nonlinear studies 16, No. 1, 85-94 (2009) · Zbl 1189.34009
[4]Kilbas, A. A.; Srivatsava, H. M.; Trujillo, J. J.: Theory and applications of fractional differential equations, (2006)
[5]F.A. McRae, Monotone iterative technique for PBVP of Caputo fractional differential equations (in press)
[6]Podlubny, I.: Fractional differential equations, (1999)
[7]Devi, J. Vasundhara: Generalized monotone technique for periodic boundary value problems of Caputo fractional differential equations, Communications in applied analysis 12, No. 4, 399-406 (2008) · Zbl 1184.34014
[8]Lakshmikantham, V.; Vatsala, A. S.: Theory of fractional differential inequalities and application, Communications in applied analysis 11, No. 3–4 (2007) · Zbl 1159.34006
[9]Lakshmikantham, V.; Vatsala, A. S.: Basic theory of fractional differential equations, Nonlinear analysis 69, No. 8, 2677-2682 (2008) · Zbl 1161.34001 · doi:10.1016/j.na.2007.08.042
[10]F.A. McRae, Monotone iterative technique and existence results for fractional differential equations (in press)