Upper and Lower Solutions Method for Darboux Problem for Fractional Order Implicit Impulsive Partial Hyperbolic Differential Equations

Abbas, Saïd   ; Benchohra, Mouffak

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 51 (2012) no. 2, pp. 5-18

Abstract (VO)

In this paper we investigate the existence of solutions for the initial value problems (IVP for short), for a class of implicit impulsive hyperbolic differential equations by using the lower and upper solutions method combined with Schauder’s fixed point theorem.

Détail

Classification : 26A33, 35A01, 35R11, 35R12
Keywords: partial hyperbolic differential equation; fractional order; left-sided mixed; Riemann–Liouville integral; mixed regularized derivative; impulse; upper solution; lower solution; fixed point

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