New concepts of fractional quantum calculus and applications to impulsive fractional q-difference equations

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• 作者：Jessada Tariboon (1)
  Sotiris K Ntouyas (2)
  Praveen Agarwal (3)
  
  1. Nonlinear Dynamic Analysis Research Center ; Department of Mathematics ; Faculty of Applied Science ; King Mongkut鈥檚 University of Technology North Bangkok ; Bangkok ; 10800 ; Thailand
  2. Department of Mathematics ; University of Ioannina ; Ioannina ; 451 10 ; Greece
  3. Department of Mathematics ; Anand International College of Engineering ; Jaipur ; 303012 ; India
  
• 关键词：26A33 ; 39A13 ; 34A37 ; quantum calculus ; impulsive fractional q ; difference equations ; existence ; uniqueness
• 刊名：Advances in Difference Equations
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,307 KB
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• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847

文摘

In this paper we define new concepts of fractional quantum calculus by defining a new q-shifting operator. After giving the basic properties we define the q-derivative and q-integral. New definitions of Riemann-Liouville fractional q-integral and q-difference on an interval \([a,b]\) are given and their basic properties are discussed. As applications of the new concepts, we prove existence and uniqueness results for first and second order initial value problems for impulsive fractional q-difference equations.