Quantum difference Langevin equation with multi-quantum numbers q-derivative nonlocal conditions

Volume 9, Issue 6, pp 3491--3503 http://dx.doi.org/10.22436/jnsa.009.06.04

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Authors

Surang Sitho - Department of Social and Applied Science, College of Industrial Technology, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand. Sorasak Laoprasittichok - 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. 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.

Abstract

In the present paper, we study a new class of boundary value problems for Langevin quantum difference equations with multi-quantum numbers q-derivative nonlocal conditions. Some new existence and uniqueness results are obtained by using standard fixed point theorems. The existence and uniqueness of solutions is established by Banach's contraction mapping principle, while the existence of solutions is derived by using Krasnoselskii's fixed point theorem and Leray-Schauder's nonlinear alternative. Examples illustrating the results are also presented.

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Keywords

• q-calculus
• nonlocal conditions
• Langevin equation
• existence
• fixed point.

MSC

•  34A08
•  26A33

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