Controllability for Impulsive Fractional Evolution Inclusions with State-Dependent Delay

Open Access

Original research article

Author(s):

Khalida Aissani^a, Mouffak Benchohra^b, Juan J. Nieto^c

^aUniversity of Bechar, P.O. Box 417, 08000, Bechar, Algeria
^bLaboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, P.O. Box 89, 22000, Sidi Bel-Abbès, Algeria; Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
^cDepartamento de Estatística, Análise Matemática e Optimización, Instituto de Matemáticas, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain

Advances in the Theory of Nonlinear Analysis and its Applications 3(1), 18-34.

Received: December 10, 2018

Accepted: February 11, 2019

Published: February 14, 2019

Abstract

In this paper, sufficient conditions are established for the controllability of impulsive fractional evolution inclusions with state-dependent delay in Banach spaces. The analysis is based on a fixed-point theorem for condensing maps due to Bohnenblust–Karlin and the theory of semigroups to derive the main results. An illustrative example is provided to demonstrate the applicability of the theoretical findings.

Keywords: Impulsive fractional evolution, α-resolvent family, solution operator, Caputo fractional derivative, mild solution, state-dependent delay, fixed point, Banach space.

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APA Style

Benchohra, M., Aissani, K., & Nieto, J. (2019). Controllability for impulsive fractional evolution inclusions with state-dependent delay. Advances in the Theory of Nonlinear Analysis and its Application, 3(1), 18-34.