Geodesic
Impulsive Partial Hyperbolic Functional Differential Equations of Fractional Order with State-Dependent Delay
Fractional calculus and applied analysis, Tome 13 (2010) no. 3, pp. 225-244.

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This paper deals with the existence and uniqueness of solutions of two classes of partial impulsive hyperbolic differential equations with fixed time impulses and state-dependent delay involving the Caputo fractional derivative. Our results are obtained upon suitable fixed point theorems.
Keywords: Impulsive Functional Differential Equations, Fractional Order Differential Equation, Left-Sided Mixed Riemann-Liouville Integral, Caputo Fractional-Order Derivative, State-Dependent Delay, Fixed Point 
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     author = {Abbas, Sa{\"\i}d and Benchohra, Mouffak},
     title = {Impulsive {Partial} {Hyperbolic} {Functional} {Differential} {Equations} of {Fractional} {Order} with {State-Dependent} {Delay}},
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Abbas, Saïd; Benchohra, Mouffak. Impulsive Partial Hyperbolic Functional Differential Equations of Fractional Order with State-Dependent Delay. Fractional calculus and applied analysis, Tome 13 (2010) no. 3, pp. 225-244. http://geodesic.mathdoc.fr/item/FCAA_2010_13_3_a0/