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Zbl 0967.45004
Momani, Shaher M.
Local and global existence theorems on fractional integro-differential equations. (English)
[J] J. Fractional Calc. 18, 81-86 (2000). ISSN 0918-5402

The author obtains local and global existence and uniqueness theorems of the fractional integro-differential equations of the type: $$x^{(\alpha)} (t)=f(t,x)+ \int^t_{t_0} k\bigl(t,s,x(s) \bigr)ds, \quad \alpha \in \bbfR,\ 0<\alpha\le 1,$$ as application of Schauder's and Tykhonov's fixed-point theorems.
[V.Lakshmikantham (Melbourne/Florida)]

MSC 2000:: *45J05 Integro-ordinary differential equations
45G10 Nonsingular nonlinear integral equations
26A33 Fractional derivatives and integrals (real functions)

Keywords: existence; fractional integro-differential equations

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