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SOOCHOW JOURNAL OF MATHEMATICS

Volume 33, No. 4, pp. 619-627, October 2007




LOCAL AND GLOBAL UNIQUENESS THEOREMS ON

FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS

VIA BIHARI'S AND GRONWALL'S INEQUALITIES


BY


SHAHER MOMANI, AHLAM JAMEEL AND SORA AL-AZAWI




Abstract. Local and global uniqueness theorems of solutions of the fractional integro-differential equations

$\displaystyle D_{*}^{\alpha}x(t)=f(t,x(t))+\int_{t_{0}}^t K(t,s,x(s))ds,\;\;
\;\; 0<\alpha \leq 1,
$

have been obtained. Our method is an application of Bihari's and Gronwall's inequalities.

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Received October 20, 2005; revised January 11, 2007.

AMS Subject Classification. 26A33, 26D10.

Key words. fractional derivatives, integro-differential equations, integral inequalities.