Impulsive first-order functional \(q_k\)-integro-difference inclusions with boundary conditions

Volume 9, Issue 1, pp 46--60 http://dx.doi.org/10.22436/jnsa.009.01.05

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Authors

Jessada Tariboon - Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, 10800, Thailand. Sotiris K. Ntouyas - Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece. - Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. Weerawat Sudsutad - Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, 10800, Thailand.

Abstract

In this paper, we discuss the existence of solutions for a first order boundary value problem for impulsive functional \(q_k\)-integro-difference inclusions. Some new existence results are obtained for convex as well as non-convex multivalued maps with the aid of some classical fixed point theorems. Illustrative examples are also presented.

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Keywords

• \(q_k\)-derivative
• \(q_k\)-integral
• impulsive \(q_k\)-difference inclusions
• existence
• fixed point theorem.

MSC

•  34A60
•  26A33
•  39A13
•  34A37

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