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Existence and Stability of Solutions for a Class of Fractional Impulsive Differential Equations with Atangana-Baleanu-Caputo Derivative

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Journal of Applied Mathematics and Physics 2023年第12期11卷 3914-3927页

作者： Xuefan Lin Weimin Hu Youhui Su yongzhen yun College of Mathematics and Statistics Yili Normal University Yining China School of Mathematics and Statistics Xuzhou University of Technology Xuzhou China Institute of Applied Mathmatics Yili Normal University Yining China

In this paper, we are concerned with the existence of solutions to a class of Atangana-Baleanu-Caputo impulsive fractional differential equation. The existence and uniqueness of the solution of the fractional differential equation are obtained by Banach and Krasnoselakii fixed point theorems, and sufficient conditions for the existence and uniqueness of the solution are also developed. In addition, the Hyers-Ulam stability of the solution is considered. At last, an example is given to illustrate the main results.

关键词： Fractional Differential Equation Fixed Point Theorem Existence of Solutions

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一类分数阶微分方程的反周期边值问题

广西师范大学学报（自然科学版） 2020年第6期38卷 56-64页

作者：左佳斌贠永震河海大学理学院江苏南京210098 吉林工程技术师范学院应用理学院吉林长春130052

研究一类具有p-Laplace算子的非线性分数阶微分方程反周期边值问题解的存在性。首先给出该边值问题的Green函数;然后利用p-Laplace算子的性质和不动点定理得到该边值问题解的存在性结果;最后给出2个例子验证得到的结果。

关键词：分数阶微分方程反周期边值问题解的存在性 p-Laplace算子

一类具有p-Laplacian算子的分数阶微分方程反周期边值问题解的存在唯一性

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数学物理学报（A辑） 2018年第6期38卷 1162-1172页

作者：贠永震苏有慧胡卫敏徐州工程学院数学与物理科学学院江苏徐州221000 伊犁师范学院数学与统计学院新疆伊宁835000

该文研究了一类具有p-Laplacian算子的非线性Caputo分数阶微分方程反周期边值问题解的存在唯一性.首先,利用分数阶微分方程和反周期边值条件给出了该边值问题的Green函数,然后利用p-Laplacian算子的性质和Banach压缩映射原理得到该边值... 详细信息

该文研究了一类具有p-Laplacian算子的非线性Caputo分数阶微分方程反周期边值问题解的存在唯一性.首先,利用分数阶微分方程和反周期边值条件给出了该边值问题的Green函数,然后利用p-Laplacian算子的性质和Banach压缩映射原理得到该边值问题解的存在唯一性结论,最后给出两个例子验证结论的合理性.值得一提的是此文研究的微分方程的反周期边值条件是带有Caputo分数阶微分.

关键词： Caputo分数阶微分反周期边值问题解的存在唯-性 p-Laplacian算子,Banach压缩映射原理

无界域上带白噪声的非自治强阻尼波动方程的动力学行为

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海南大学学报（自然科学版） 2019年第2期37卷 89-100页

作者：王苗苗贠永震河海大学理学院

研究了无界域上带有强阻尼和可加噪声的非自治随机波动方程随机吸引子的存在性,其中非线性阻尼具有临界立方增长指数,然后通过对变换系统解的一致估计,得到渐近紧的D-拉回吸收集的存在性,最后得到原系统随机吸引子的存在性.

关键词：波动方程随机吸引子渐近紧性非线性阻尼

一类带有p-Laplacian算子的分数阶微分方程反周期边值问题解的存在性

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宁夏大学学报（自然科学版） 2017年第1期38卷 5-8,14页

作者：贠永震苏有慧胡卫敏伊犁师范学院数学与统计学院新疆伊宁835000 徐州工程学院数学与物理科学学院江苏徐州221111

研究了一类带有p-Laplacian算子的分数阶微分方程反周期边值问题{(Cφp Dα0+u(t))=f(t,u(t)),t∈[0,T],u(0)=-u(T),u′(0)=-u′(T)解的存在性,其中10,φp(s)=s p-1s,p>1,(φp)-1=φq,p-1+q-1=1,CDα0+为Caputo分数阶微分,f:[0,T]×R→R为连续函数.利用分数阶微分方程和反周期边值条件的特性给出所研究边值问题的Green’s函数,然后借助于Banach压缩映像原理和Krasnosel’skiis不动点定理得到此反周期边值问题解的一些新的存在性理论.作为应用,给出了2个例子验证了所得结果.

关键词：分数阶微分方程反周期边值问题解的存在性 p-Laplacian算子

TiB_(2)含量对TiB_(x)/Ti合金涂层组织及摩擦学性能的影响

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表面技术 2024年第11期53卷 140-149页

作者：寇斐凡岳赟杜志浩杜三明陈德强张永振高端轴承摩擦学技术与应用国家地方联合工程实验室河南洛阳471023 河南科技大学材料科学与工程学院河南洛阳471023

目的在Ti-47Zr-5Al-3V(以下简称T47Z)表面制备TiB_(x)/Ti合金复合涂层,以提高合金的摩擦学性能。方法采用等离子弧熔覆技术在T47Z合金表面熔覆不同配比的(TiB_(2)+Ti)粉末,制备TiB_(x)陶瓷相增强钛合金复合涂层,使用扫描电镜(SEM)、X射... 详细信息

目的在Ti-47Zr-5Al-3V(以下简称T47Z)表面制备TiB_(x)/Ti合金复合涂层,以提高合金的摩擦学性能。方法采用等离子弧熔覆技术在T47Z合金表面熔覆不同配比的(TiB_(2)+Ti)粉末,制备TiB_(x)陶瓷相增强钛合金复合涂层,使用扫描电镜(SEM)、X射线衍射仪(XRD)、维氏硬度显微计和UMT-2摩擦磨损试验机对涂层微观组织、硬度及摩擦磨损性能进行测试研究。结果涂层厚度约2 mm,无裂纹、气孔等缺陷,涂层的基体组织为α相,针状、棒状的TiB增强相和颗粒状的TiB_(2)增强相均匀分布于α相中。随着TiB_(2)含量的增加,涂层基体组织无明显变化,增强相的数量增加,尺寸逐渐变大。涂层的表面硬度最高可达893.4HV0.2,约为基体的2.07倍。涂层的耐磨性相较基体均获得不同程度的提升,当TiB_(2)的质量分数为40%时,涂层的耐磨性提升最为显著,相较基体提高了53.7%。T47Z合金的磨损机理为严重的黏着磨损和磨粒磨损。TiB_(2)的质量分数为10%的涂层,其磨损机理以黏着磨损为主,磨粒磨损为辅。随着TiB_(2)含量的增加,涂层的磨损机制逐渐转向磨粒磨损。结论通过控制粉体中TiB_(2)的含量,能够利用等离子弧熔覆技术在钛合金表面制备TiB_(x)/Ti合金复合涂层,尤其当TiB_(2)的质量分数为40%时,涂层的硬度及耐磨性能均获得大幅度提升。因此,运用等离子熔覆技术制备陶瓷相增强金属基复合涂层可切实有效地提高钛合金的硬度及耐磨性能。

关键词：钛合金等离子弧熔覆显微组织涂层硬度摩擦磨损性能

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Hybrid-cavity semiconductor lasers with a whispering-gallery cavity for controlling Q factor

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Science China(Information Sciences) 2018年第8期61卷 5-17页

作者： yongzhen HUANG Xiuwen MA Yuede YANG Jinlong XIAO yun DU State Key Laboratory on Integrated Optoelectronics Institute of Semiconductors & College of Materials Science and Optoelectronic Technology University of Chinese Academy of SciencesChinese Academy of Sciences

Hybrid cavities composed of a Fabry-P′erot(FP) cavity and a whispering-gallery mode(WGM)microcavity have been proposed and demonstrated for modulating mode Q factor to realize single mode and optical bistable lasers. In this article, we report hybrid cavity lasers with a pentagon microcavity and a square microcavity, respectively. The reflectivity spectra of different microcavities are simulated to select microcavities for hybrid cavities. Mode coupling with mode Q factor enhancement is investigated numerically and experimentally. Stable single mode operations with a high coupling efficiency to a single mode fiber are realized for a hybrid cavity laser with a square microcavity. Furthermore, optical bistability hybrid lasers are investigated as the microcavity is unbiased, due to saturable absorption in the microcavity and mode competition, respectively. All-optical flip-flop is demonstrated using trigger optical pulses with a width of100 ps for mode competition bistability. The stable single mode operation and optical bistability of hybrid cavity lasers may shed light on the applications for photonic integrated circuits and optical signal processing.

关键词： optical microcavity semiconductor lasers hybrid cavity optical bistability single mode laser

Output characteristics of square and circular resonator microlasers connected with two output waveguides

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Science China Technological Sciences 2013年第3期56卷 538-542页

作者： HUANG yongzhen Lü XiaoMeng LIN JianDong DU yun State Key Laboratory on Integrated Optoelectronics Institute of SemiconductorsChinese Academy of Sciences

Square and circular resonator microlasers connected with two output waveguides are investigated for correlation of output powers from the two output *** square resonator microlasers with two output waveguides connected at the midpoint of one side and one vertex are fabricated and tested by measuring the output power versus injection current and the laser spectra of the two *** laser spectra indicated that the output power correlation between the two output ports is very weak because of different lasing modes in different ports of the square *** resonator microlaser with two output waveguides can realize single mode operation and has good output correlation from the two *** the output power from one port of the circular microlasers can be monitored by that of another port.

关键词： AlGaInAs/InP semiconductor microlasers square resonator microlasers circular resonator microlasers

Whispering-gallery microcavity semiconductor lasers suitable for photonic integrated circuits and optical interconnects

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Science China(Technological Sciences) 2009年第12期52卷 3447-3453页

作者： HUANG yongzhen YANG YueDe WANG ShiJiang XIAO JinLong CHE KaiJun DU yun State Key Laboratory on Integrated Optoelectronics Institute of SemiconductorsChinese Academy of SciencesPO Box 912Beijing 100083China

The characteristics of whispering-gallery-like modes in the equilateral triangle and square microresonators are introduced,including directional emission triangle and square microlasers connected to an output *** propose a photonic interconnect scheme by connecting two directional emission microlasers with an optical waveguide on silicon integrated circuit *** measurement indicates that the triangle microlasers can work as a resonance enhanced photodetector for optical interconnect.

关键词： optical microcavity microlaser resonance mode optical interconnect