Lyapunov-type inequality for a fractional differential equation with fractional boundary conditions

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• 作者：Ji Rong (1) (2)
  Chuanzhi Bai (1)
  
  1. Department of Mathematics ; Huaiyin Normal University ; Huaian ; Jiangsu ; 223300 ; P.R. China
  2. Department of Mathematics ; Jiangsu Normal University ; Xuzhou ; Jiangsu ; 221116 ; P.R. China
  
• 关键词：34A08 ; 34A40 ; 26D10 ; 33E12 ; Lyapunov inequality ; Caputo fractional derivative ; Mittag ; Leffler function
• 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：933 KB
• 参考文献：1. Lyapunov, AM (1907) Probl猫me g茅n茅ral de la stabilit茅 du mouvement. Ann. Fac. Sci. Univ. Toulouse 2: pp. 203-407
  2. Brown, RC, Hinton, DB Lyapunov inequalities and their applications. In: Rassias, TM eds. (2000) Survey on Classical Inequalities. Kluwer Academic, Dordrecht, pp. 1-25 CrossRef
  3. Pachpatte, BG (2005) Mathematical Inequalities. Elsevier, Amsterdam
  4. Tiryaki, A (2010) Recent developments of Lyapunov-type inequalities. Adv. Dyn. Syst. Appl. 5: pp. 231-248
  5. Cakmak, D, Tiryaki, A (2010) Lyapunov-type inequality for a class of Dirichlet quasilinear systems involving the ( p 1 , p 2 , 鈥, p n ) $(p_{1}, p_{2},\ldots, p_{n})$ -Laplacian. J. Math. Anal. Appl. 369: pp. 76-81 CrossRef
  6. Tang, XH, He, X (2012) Lower bounds for generalized eigenvalues of the quasilinear systems. J. Math. Anal. Appl. 385: pp. 72-85 CrossRef
  7. Yang, X, Kim, Y, Lo, K (2012) Lyapunov-type inequality for a class of linear differential systems. Appl. Math. Comput. 219: pp. 1805-1812 CrossRef
  8. Yang, X, Kim, Y, Lo, K (2010) Lyapunov-type inequality for a class of odd-order differential equations. J. Comput. Appl. Math. 234: pp. 2962-2968 CrossRef
  9. Sanchez, J, Vergara, V (2011) A Lyapunov-type inequality for a 蠄-Laplacian operator. Nonlinear Anal. 74: pp. 7071-7077 CrossRef
  10. Ferreira, RAC (2014) On a Lyapunov-type inequality and the zeros of a certain Mittag-Leffler function. J. Math. Anal. Appl. 412: pp. 1058-1063 CrossRef
  11. Ferreira, RAC (2013) A Lyapunov-type inequality for a fractional boundary value problem. Fract. Calc. Appl. Anal. 16: pp. 978-984 CrossRef
  12. Jleli, M, Samet, B (2015) Lyapunov-type inequalities for a fractional differential equation with mixed boundary conditions. Math. Inequal. Appl. 18: pp. 443-451
  13. Podlubny, I (1999) Fractional Differential Equations. Academic Press, San Diego
  14. Zhang, S (2006) Positive solutions for boundary-value problems of nonlinear fractional differential equations. Electron. J.聽Differ. Equ. 2006:
  15. Abramowitz, M, Stegun, I (1972) Handbook of Mathematical Functions. Dover, New York
  16. Miller, KS, Ross, B (1993) An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York
  17. Duan, JS, Wang, Z, Liu, YL, Qiu, X (2013) Eigenvalue problems for fractional ordinary differential equations. Chaos Solitons Fractals 46: pp. 46-53 CrossRef
  
• 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, a Lyapunov-type inequality is obtained for a fractional differential equation under fractional boundary conditions. We then use this inequality to obtain an interval where a certain Mittag-Leffler function has no real zeros.