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On Fractional Neutral Integro-differential Systems with State-dependent Delay in Banach Spaces

100%

Kailasavalli S. , Suganya S. , Mallika Arjunan M.

tom Vol. 151, nr 1/4

109--133

Based on concepts for semigroups, fractional calculus, resolvent operator and Banach contraction principle, this manuscript is principally involved with existence results for fractional neutral integro-differential systems with state-dependent delay in Banach spaces. To acquire the main results, our working concepts are that the functions deciding the equation fulfill certain Lipschitz conditions of local type which is similar to the hypotheses [1]. Finally an examples are additionally offered to exhibit the achieved hypotheses.

Semilinear functional differential equations of fractional order with state-dependent delay

86%

Benchohra M. , Bennihi O. , Ezzinbi K.

Commentationes Mathematicae

2013

tom Vol 53, No. 1

47--59

In this paper we provide sufficient conditions for the existence and uniqueness of mild solutions for a class of semilinear functional differential equations of fractional order with state-dependent delay. The nonlinear alternative of Frigon- Granas type for contractions maps in Fr´echet spaces combined with -resolvent family is the main tool in our analysis.

Fractional integro-differential inclusions with state-dependent delay

86%

Aissani K. , Benchohra M. , Ezzinbi K.

nr 2

153-167

In this paper, we establish sufficient conditions for the existence of mild solutions for fractional integro-differential inclusions with state-dependent delay. The techniques rely on fractional calculus, multivalued mapping on a bounded set and Bohnenblust-Karlin's fixed point theorem. Finally, we present an example to illustrate the theory.

Controllability of multi-term time-fractional differential systems with state-dependent delay

72%

Chaudhary R. , Singh V. , Pandey D. N.

2020

tom Vol. 26, nr 2

241--255

In this paper, controllability results for a class of multi-term time-fractional differential systems with state-dependent delay have been studied. The concept of fractional calculus, measure of noncompactness and Mönch fixed-point theorem has been implemented to obtain a new set of controllability results. Finally, an application is given to illustrate the obtained results.

Measure of noncompactness and neutral functional differential equations with state-dependent delay

58%

Benchohra M. , Henderson J. , Medjadj I.

Journal of Mathematics and Applications

2016

tom Vol. 39

23--45

Our aim in this work is to study the existence of solutions of first and second order for neutral functional differential equations with state-dependent delay. We use the Mönch’s fixed point theorem for the existence of solutions and the concept of measures of noncompactness.