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Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations. (English) Zbl 1201.34008
Considered are existence and uniqueness of solutions of the following initial value problems
\[ D^\alpha x(t)=f(t,D^\beta x(t)),\, 0<t\leq 1;\quad x^{(k)}=n_k,\,k=0,1,\dots,m-1, \] where \(m-1<\alpha<m,\) \(n-1<\beta<n\) \((m,n\in \mathbb{N},\,m-1>n)\), \(D^\alpha\) stands for the Caputo derivative of order \(\alpha\) and \(f\) is a continuous function defined on \([0,1]\times \mathbb{R}\). The proofs are achieved by means of the contraction mapping principle.

34A08 Fractional ordinary differential equations and fractional differential inclusions
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
Full Text: DOI
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