Lyapunov inequalities of nested fractional boundary value problems and applications

IF 0.3 Q4 MATHEMATICS
Yousef Gholami
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引用次数: 2

Abstract

In this paper, we study certain classes of nested fractional boundary value problems including both of the Riemann–Liouville and Caputo fractional derivatives. In addition, since we will use the signed-power operators ϕνz|z|ν1z,ν(0,) in the governing equations, so our desired boundary value problems possess half-linear nature. Our investigation theoretically reaches so called Lyapunov inequalities of the considered nested fractional boundary value problems, while in viewpoint of applicability using the obtained Lyapunov inequalities we establish some qualitative behavior criteria for nested fractional boundary value problems such as a disconjugacy criterion that will also be used to establish nonexistence results, upper bound estimation for maximum number of zeros of the nontrivial solutions and distance between consecutive zeros of the oscillatory solutions. Also, considering corresponding nested fractional eigenvalue problems we find spreading interval of the eigenvalues.

嵌套分数边值问题的Lyapunov不等式及其应用
本文研究了一类包含Riemann-Liouville和Caputo分数阶导数的嵌套分数阶边值问题。另外,由于我们将在控制方程中使用有符号幂算子ϕνz |z|ν−1z,ν∈(0,∞),所以我们期望的边值问题具有半线性性质。我们的研究在理论上达到了所考虑的嵌套分数边值问题的所谓Lyapunov不等式,而从适用性的角度来看,我们利用得到的Lyapunov不等式建立了嵌套分数边值问题的一些定性行为准则,如解共轭准则,该准则也将用于建立不存在性结果。非平凡解的最大零点数和振荡解的连续零点距离的上界估计。同时,考虑相应的嵌套分数阶特征值问题,找到了特征值的扩展区间。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
0.50
自引率
50.00%
发文量
0
审稿时长
22 weeks
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