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Local and global existence theorems on fractional integro-differential equations. (English) Zbl 0967.45004

The author obtains local and global existence and uniqueness theorems of the fractional integro-differential equations of the type: \[ x^{(\alpha)} (t)=f(t,x)+ \int^t_{t_0} k\bigl(t,s,x(s) \bigr)ds, \quad \alpha \in \mathbb{R},\;0<\alpha\leq 1, \] as application of Schauder’s and Tykhonov’s fixed-point theorems.

MSC:

45J05 Integro-ordinary differential equations
45G10 Other nonlinear integral equations
26A33 Fractional derivatives and integrals
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