, Volume 15, Issue 2, pp 168-182

On fractional order derivatives and Darboux problem for implicit differential equations

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Abstract

In this paper we prove some relations between the Riemann-Liouville and the Caputo fractional order derivatives, and we investigate the existence and uniqueness of solutions for the initial value problems (IVP for short), for a class of functional hyperbolic differential equations by using some fixed point theorems.