Green’s functions, positive solutions, and a Lyapunov inequality for a caputo fractional-derivative boundary value problem-Reference-Cited by-同舟云学术

Green’s functions, positive solutions, and a Lyapunov inequality for a caputo fractional-derivative boundary value problem

Published:2019-06-01 Issue:3 Volume:22 Page:750-766
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Meng Xiangyun¹,Stynes Martin¹

Affiliation:

1. Division of Applied and Computational Mathematics Beijing Computational Science , Research Center Building 9, East Zone, ZPark II, No.10 Xibeiwang East Road Haidian District , Beijing , 100193 , China

Abstract

Abstract We consider a nonlinear boundary problem whose highest-order derivative is a Caputo derivative of order α with 1 < α < 2. Properties of its associated Green’s function are derived. These properties enable us to deduce sufficient conditions for the existence of a positive solution to the boundary value problem and to prove a Lyapunov inequality for the problem. Our results sharpen and extend earlier results of other authors.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2019-0041/pdf

Reference17 articles.

1. Z. Bai, H. Lü, Positive solutions for boundary value problem of nonlinear fractional differential equation. J. Math. Anal. Appl. 311, No 2 (2005), 495–505.

2. A. Chidouh, D. Torres, A generalized Lyapunov’s inequality for a fractional boundary value problem. J. Comput. Appl. Math. 312 (2017), 192–197.

3. K. Diethelm, The Analysis of Fractional Differential Equations. Springer-Verlag, Berlin (2010).

4. Rui A.C. Ferreira, Lyapunov-type inequality for a fractional boundary value problem. Fract. Calc. Appl. Anal. 16, No 4 (2013), 978–984; 10.2478/s13540-013-0060-5; https://www.degruyter.com/view/j/fca.2013.16.issue-4/issue-files/fca.2013.16.issue-4.xml.

5. Rui A.C. Ferreira, On a Lyapunov-type inequality and the zeros of a certain Mittag-Leffler function. J. Math. Anal. Appl. 412, No 2 (2014), 1058–1063.

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