Applied Mathematics and Computation 266 (2015) 54–69 Contents lists available at ScienceDirect Applied Mathematics and Computation journal homepage: www.elsevier.com/locate/amc Existence results for an impulsive fractional integro-differential equation with state-dependent delay S. Suganya a , M. Mallika Arjunan a,∗ , J.J. Trujillo b a Department of Mathematics, C.B.M. College, Kovaipudur, Coimbatore 641042, Tamil Nadu, India b Departamento de Análisis Matemático, University of La Laguna, 38271 La Laguna, Tenerife, Spain article info MSC: 34K05 26A33 34A12 35R12 45J05 Keywords: Fractional order differential equations Impulsive conditions State-dependent delay Fixed point theorems Semigroup theory abstract In this paper, we have a tendency to implement different fixed point theorem [ Banach con- traction principle, Krasnoselskii’s [18] and Schaefer’s [, 18] coupled with solution operator to analyze the existence and uniqueness results for an impulsive fractional integro-differential equations (IFIDE) with state-dependent delay (SDD) in Banach spaces. Finally, cases are of- fered to demonstrate the concept. © 2015 Elsevier Inc. All rights reserved. 1. Introduction The concept of semigroups of bounded linear operator is meticulously associated to solving differential and integro- differential equations in Banach spaces. Recently, this concept has been employed to a significant type of non-linear differential equations in Banach spaces. For more points of interest on this concept, we allude the reader to Pazy [1]. The investigation of impulsive functional differential or integro-differential frameworks is signed up with to their application in strengthening tech- niques and phenomena conditional on short-time perturbations in the course of their progress. The perturbations are conducted separately and their term is insignificant in correlation with the aggregate length of time of the procedures. For additional pur- poses of enthusiasm on this concept and on its uses, see for example the treatise by Lakshmikantham et al. [2], Stamova [3], Graef et al. [4], Bainov and Covachev [5], Benchohra et al. [6] and the papers [7–16], and the references cited therein. The concept of fractional differential equations is growing as an essential place of research due to the fact it is better in problems in evaluation with the corresponding concept of traditional differential equations [17–19]. In fact, such designs can be regarded as an effective substitute to the traditional nonlinear differential designs to imitate many complicated procedures. In latest years, as the historical specialized mathematicians predicted, fractional differential equations have been discovered to be a highly effective tool in many areas, such as viscoelasticity, electro-chemistry, control, porous media, and electromagnetic. For fundamental certainties about fractional systems, one can make reference to the books [20–24], and the papers [25–41], and the references cited therein. Fractional equation with delay features happen in several areas such as medical and physical with state- dependent delay or non-constant delay. These days, existence results of mild solutions for such problems became very attractive ∗ Corresponding author. Tel.: +918124607098. E-mail addresses: selvarajsuganya2014@yahoo.in (S. Suganya), arjunphd07@yahoo.co.in, arjunphd2007@yahoo.co.in (M. Mallika Arjunan), jtrujill@ullmat.es (J.J. Trujillo). http://dx.doi.org/10.1016/j.amc.2015.05.031 0096-3003/© 2015 Elsevier Inc. All rights reserved.