ON HADAMARD FRACTIONAL CALCULUS
ON HADAMARD FRACTIONAL CALCULUS
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关于哈达玛分数阶微积分
DOI：
10.1142/s0218348x17500335
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发表时间：
2017-06-01
影响因子：
4.7
通讯作者：
Li, Changpin
中科院分区：
文献类型：
--
作者：
Ma, Li;Li, Changpin
本文从三个方面对阿达玛分数阶微积分进行了研究。首先，我们研究了hadamard型分数算子的半群和互反性质。然后，利用Banach收缩映射原理，给出了一类hadamard型分数阶微分方程的确定条件。最后，我们证明了一个具有弱奇异性的新的Gronwall不等式，并分析了HTFDEs的解与导数阶数和扰动项的依赖关系以及所提出的初值条件。并给出了实例说明。
This paper is devoted to the investigation of the Hadamard fractional calculus in three aspects. First, we study the semigroup and reciprocal properties of the Hadamard-type fractional operators. Then, the definite conditions of certain class of Hadamard-type fractional differential equations (HTFDEs) are proposed through the Banach contraction mapping principle. Finally, we prove a novel Gronwall inequality with weak singularity and analyze the dependence of solutions of HTFDEs on the derivative order and the perturbation terms along with the proposed initial value conditions. The illustrative examples are presented as well.