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Article

Abbas, Saïd ; Benchohra, Mouffak
Upper and Lower Solutions Method for Darboux Problem for Fractional Order Implicit Impulsive Partial Hyperbolic Differential Equations. (English). Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, vol. 51 (2012), issue 2, pp. 5-18
MSC: 26A33, 35A01, 35R11, 35R12 | MR 3058869 | Zbl 06204926
Keywords:
partial hyperbolic differential equation; fractional order; left-sided mixed; Riemann–Liouville integral; mixed regularized derivative; impulse; upper solution; lower solution; fixed point
Summary:
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.
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