Geodesic
A global uniqueness result for fractional order implicit differential equations
Commentationes Mathematicae Universitatis Carolinae, Tome 53 (2012) no. 4, pp. 605-614.

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In this paper we investigate the global existence and uniqueness of solutions for the initial value problems (IVP for short), for a class of implicit hyperbolic fractional order differential equations by using a nonlinear alternative of Leray-Schauder type for contraction maps on Fréchet spaces.
Classification : 26A33
Keywords: partial hyperbolic differential equation; fractional order; left-sided mixed Riemann-Liouville integral; mixed regularized derivative; solution; Fréchet space; fixed point 
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Abbas, Said; Benchohra, Mouffak. A global uniqueness result for fractional order implicit differential equations. Commentationes Mathematicae Universitatis Carolinae, Tome 53 (2012) no. 4, pp. 605-614. http://geodesic.mathdoc.fr/item/CMUC_2012__53_4_a7/