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Existence results for boundary value problems of nonlinear fractional differential equations. (English) Zbl 1231.34007
Summary: We consider the existence of solutions for the nonlinear fractional differential equation with the boundary value conditions where and are the standard Caputo derivative with $1<\alpha \le 2$, $r\ne 0$. By using the contraction mapping principle and the Schauder fixed point theorem, some existence results are obtained. In addition, Lemma 2.6 in this paper is a valuable tool in seeking solvability of the fractional differential equations.

##### MSC:
 34A08 Fractional differential equations 45J05 Integro-ordinary differential equations
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##### References:
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