Existence results for impulsive fractional q-difference equations with anti-periodic boundary conditions

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• 作者：Bashir Ahmad ; Jessada Tariboon ; Sotiris K Ntouyas…
• 关键词：26A33 ; 39A13 ; 34A37 ; quantum calculus ; impulsive fractional q ; difference equations ; existence ; uniqueness ; fixed point theorem
• 刊名：Boundary Value Problems
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：2016
• 期：1
• 全文大小：1,607 KB
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  7. Graef, JR, Kong, L: Positive solutions for a class of higher order boundary value problems with fractional q-derivatives. Appl. Math. Comput. 218, 9682-9689 (2012) MATH MathSciNet CrossRef
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• 作者单位：Bashir Ahmad (1)
  Jessada Tariboon (2)
  Sotiris K Ntouyas (1) (3)
  Hamed H Alsulami (1)
  Shatha Monaquel (1)
  
  1. 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
  2. Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, 10800, Thailand
  3. Department of Mathematics, University of Ioannina, Ioannina, 451 10, Greece
  
• 刊物主题：Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations; Analysis; Approximations and Expansions; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1687-2770

文摘

This paper studies a Caputo type anti-periodic boundary value problem of impulsive fractional q-difference equations involving a q-shifting operator of the form \({}_{a}\Phi_{q}(m) = qm + (1-q)a\). Concerning the existence of solutions for the given problem, two theorems are proved via Schauder’s fixed point theorem and the Leray-Schauder nonlinear alternative, while the uniqueness of solutions is established by means of Banach’s contraction mapping principle. Finally, we discuss some examples illustrating the main results. Keywords quantum calculus impulsive fractional q-difference equations existence uniqueness fixed point theorem