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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.
MSC:
34A08Fractional differential equations
26A33Fractional derivatives and integrals (real functions)
45J05Integro-ordinary differential equations
References:
[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)