Received: 23 February 2019 DOI: 10.1002/mma.6020 SPECIAL ISSUE PAPER The Henstock-Kurzweil-Pettis integral and multiorders fractional differential equations with impulses and multipoint fractional integral boundary conditions in Banach spaces Djamila Seba 1 Sadek Habani 1 Abbes Benaissa 2 Hamza Rebai 3 1 Dynamic of Engines and Vibroacoustic Laboratory, University M'Hamed Bougara of Boumerdes, Boumerdes, Algeria 2 Laboratory of Analysis and Control of PDEs, Sidi Bel-Abbès University, Sidi Bel-Abbès, Algeria 3 Laboratory of Dynamic Systems, University of Sciences and Technology Houari Boumediene, USTHB, Bab Ezzouar, Algeria Correspondence Djamila Seba, Dynamic of Engines and Vibroacoustic Laboratory, University M'Hamed Bougara of Boumerdes, Boumerdes, Algeria. Email: seba@univ-boumerdes.dz Communicated by: T.E. Simos Present address Dynamic of Engines and Vibroacoustic Laboratory, Faculty of Engineer's Sciences, University M'Hamed Bougara of Boumerdes, Boumerdes, Algeria This paper is devoted to the existence of weak solutions for a multipoint fractional integral boundary value problem of an impulsive nonlinear differential equation involving multiorders fractional derivatives and deviat- ing argument. We make use of an appropriate fixed point theorem combined with the technique of measures of weak noncompactness. Our investigation is considered in a Banach space. The applicability of the obtained results is illustrated by an example. KEYWORDS Banach space, boundary value problem, Caputo fractional derivative, fixed point, Henstock-Kurzweil-Pettis integral, measure of weak noncompactness MSC CLASSIFICATION 26A33; 34B37; 34G20 1 INTRODUCTION Impulsive differential equations are one of the important areas of research because of their ability to model many real processes and phenomena studied in control theory, mechanics, biology, biotechnologies, medicine, economics, etc. Indeed, they are used to describe the dynamics of many evolutionary processes subject to short-time perturbations.The perturbations are considered to take place instantaneously in the form of impulses as they are performed discretely and their duration, compared with the total duration of the processes and phenomena, is negligible. Among the different approaches to the investigation of impulsive differential equations, we are interested in the one based on the application of the classical methods of the theory of ordinary differential equations. In this direction, the works by Mil'man and Myshkis 1,2 and Myshkis and Samoilenko 3 were the first in which the general concepts of the theory of systems with pulse action are formulated from a new point of view and their basic specific features are investigated. The growing interest of many authors in the investigation of impulsive differential equations nowadays is due to their Math Meth Appl Sci. 2019;1–18. wileyonlinelibrary.com/journal/mma © 2019 John Wiley & Sons, Ltd. 1