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Mathematics 2017, 5(1), 9; doi:10.3390/math5010009

Existence of Mild Solutions for Impulsive Fractional Integro-Differential Inclusions with State-Dependent Delay

Department of Mathematics, C. B. M. College, Kovaipudur, Coimbatore 641 042, Tamil Nadu, India
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Author to whom correspondence should be addressed.
Academic Editor: Rui A.C. Ferreira
Received: 15 October 2016 / Revised: 4 January 2017 / Accepted: 17 January 2017 / Published: 25 January 2017
(This article belongs to the Special Issue Fractional Differential and Difference Equations)
View Full-Text   |   Download PDF [277 KB, uploaded 14 March 2017]

Abstract

In this manuscript, we implement Bohnenblust–Karlin’s fixed point theorem to demonstrate the existence of mild solutions for a class of impulsive fractional integro-differential inclusions (IFIDI) with state-dependent delay (SDD) in Banach spaces. An example is provided to illustrate the obtained abstract results. View Full-Text
Keywords: Fractional order differential equations; impulsive conditions; state-dependent delay (SDD); multivalued map; fixed point theorem; Banach space; semigroup theory Fractional order differential equations; impulsive conditions; state-dependent delay (SDD); multivalued map; fixed point theorem; Banach space; semigroup theory
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Suganya, S.; Mallika Arjunan, M. Existence of Mild Solutions for Impulsive Fractional Integro-Differential Inclusions with State-Dependent Delay. Mathematics 2017, 5, 9.

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