Analysis of positive solution and Hyers‐Ulam stability for a class of singular fractional differential equations with p‐Laplacian in Banach space
Analysis of positive solution and Hyers‐Ulam stability for a class of singular fractional differential equations with p‐Laplacian in Banach space
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DOI：
10.1002/mma.4835
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发表时间：
2018-06
影响因子：
2.9
通讯作者：
H. Khan;Wen Chen;Hongguang Sun
中科院分区：
文献类型：
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作者：
H. Khan;Wen Chen;Hongguang Sun
研究了一类Caputo意义下含非线性p-Laplacian算子的奇异分数阶微分方程正解的存在性和Hyers-Ulam稳定性.为此，通过绿色函数Hε（t，s）将问题转化为积分方程，其中ε∈（n−1，n]，n≥4.然后，检查绿色函数是增加还是减少以及是正函数还是负函数。在这些性质之后，一些经典的不动点定理被用来证明正解的存在性。也考虑了所提出问题的Hyers-Ulam稳定性。对于结果的应用，包括一个富有表现力的例子。
This paper deals with 2 core aspects of fractional calculus including existence of positive solution and Hyers‐Ulam stability for a class of singular fractional differential equations with nonlinear p‐Laplacian operator in Caputo sense. For these aims, the suggested problem is converted into an integral equation via Green function Hε(t,s) , for ε∈(n−1,n], where n≥4. Then, the Green function is examined whether it is increasing or decreasing and positive or negative function. After these properties, some classical fixed‐point theorems are used for the existence of positive solution. Hyers‐Ulam stability of the proposed problem is also considered. For the application of the results, an expressive example is included.