New results on fractional neutral integro-differential systems with state-dependent delay via resolvent operators
Journal Title: Discussiones Mathematicae Differential Inclusions Control and Optimization - Year 2017, Vol 37, Issue 1
Abstract
In this manuscript, we set up sufficient conditions for existence and uniqueness of solutions for fractional neutral integro-differential systems (FNIDS) with state-dependent delay (SDD) in Banach spaces. Our methodology depends on resolvent operators, the Banach contraction principle, the Leray-Schauder nonlinear alternative and Schaefer's fixed point theorem. To obtain our results, our working hypotheses are that the functions determining the equation satisfy certain Lipschitz conditions of local type. An illustration is additionally provided to demonstrate the obtained theories.
Authors and Affiliations
Duraisamy Mallika, Dumitru Baleanu, Selvaraj Suganya, Mani Mallika Arjunan
Keywords
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