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Existence of solutions for impulsive fractional partial neutral integro-differential inclusions with state-dependent delay in Banach spaces

Zuomao Yan, Hongwu Zhang (2014)

Annales Polonici Mathematici

We study the existence of mild solutions for a class of impulsive fractional partial neutral integro-differential inclusions with state-dependent delay. We assume that the undelayed part generates an α-resolvent operator and transform it into an integral equation. Sufficient conditions for the existence of solutions are derived by means of the fixed point theorem for discontinuous multi-valued operators due to Dhage and properties of the α-resolvent operator. An example is given to illustrate the...

Impulsive Partial Hyperbolic Functional Differential Equations of Fractional Order with State-Dependent Delay

Abbas, Saïd, Benchohra, Mouffak (2010)

Fractional Calculus and Applied Analysis

MSC 2010: 26A33, 34A37, 34K37, 34K40, 35R11This 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.

On the oscillation of some impulsive parabolic equations with several delays

R. Atmania, S. Mazouzi (2011)

Archivum Mathematicum

In this paper, several oscillation criteria are established for some nonlinear impulsive functional parabolic equations with several delays subject to boundary conditions. We shall mainly use the divergence theorem and some corresponding impulsive delayed differential inequalities.

Ulam Stabilities for Partial Impulsive Fractional Differential Equations

Saïd Abbas, Mouffak Benchohra, Juan J. Nieto (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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.

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

Saïd Abbas, Mouffak Benchohra (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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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