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1
Controllability of multi-term time-fractional differential systems with state-dependent delay
Chaudhary Renu, Singh Vikram, Pandey D. N.
Journal of Applied Analysis
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2020
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Vol. 26, nr 2
241--255
EN
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.
2
Content available remote On Fractional Neutral Integro-differential Systems with State-dependent Delay in Banach Spaces
Kailasavalli S., Suganya S., Mallika Arjunan M.
Fundamenta Informaticae
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2017
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Vol. 151, nr 1/4
109--133
EN
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.
3
Content available Measure of noncompactness and neutral functional differential equations with state-dependent delay
Benchohra M., Henderson J., Medjadj I.
Journal of Mathematics and Applications
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2016
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Vol. 39
23--45
EN
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.
4
Content available Existence and controllability results for damped second order impulsive functional differential systems with state-dependent delay
Arjunan M. M., Nadaf N. Y.
Opuscula Mathematica
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2014
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Vol. 34, no. 3
503--522
EN
In this paper, we investigate the existence and controllability of mild solutions for a damped second order impulsive functional differential equation with state-dependent delay in Banach spaces. The results are obtained by using Sadovskii’s fixed point theorem combined with the theories of a strongly continuous cosine family of bounded linear operators. Finally, an example is provided to illustrate the main results.
5
Content available remote Semilinear functional differential equations of fractional order with state-dependent delay
Benchohra M., Bennihi O., Ezzinbi K.
Commentationes Mathematicae
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2013
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Vol 53, No. 1
47--59
EN
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.
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