Abstract: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 Fr\'echet spaces.
Keywords: partial hyperbolic differential equation, fractional order, left-sided mixed Riemann-Liouville integral, mixed regularized derivative, solution, Fr\'echet space, fixed point
AMS Subject Classification: 26A33