刘玉记.一类含高阶Riemann-Liouville型分数阶导数脉冲微分方程的通解[J].数学研究及应用,2020,40(2):140~164
一类含高阶Riemann-Liouville型分数阶导数脉冲微分方程的通解
General Solutions of a Higher Order Impulsive Fractional Differential Equation Involving the Riemann-Liouville Fractional Derivatives
投稿时间:2018-12-03  修订日期:2019-09-03
DOI:10.3770/j.issn:2095-2651.2020.02.004
中文关键词:  高阶分数阶微分方程  分片连续解  Riemann-Liouville型分数阶导数  脉冲
英文关键词:higher order fractional differential equation  piecewise continuous solution  Riemann-Liouville fractional derivative  impulse effect
基金项目:广东省自然科学基金(Grant No.S2011010001900),广东省高校自然科学基金项目(Grant No.2014KTSCX126),广州市科技项目(Grant Nos.201707010425; 201804010350).
作者单位
刘玉记 广东财经大学数学与统计学院, 广东 广州 510320 
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中文摘要:
      本文首先运用迭代法获得一类含多项Riemann-Liouville型分数阶导数的微分方程的连续通解,然后应用数学归纳法得到这类脉冲微分方程的分片连续通解. 所得结果归结于脉冲分数阶微分方程领域,对分数阶微分方程研究者有参考意义.
英文摘要:
      We give general solutions (the explicit solutions) of a class of multi-term impulsive fractional differential equations involving the Riemann-Liouville fractional derivatives. This paper contributes within the domain of impulsive fractional differential equations. The author strongly believes that the article will highly be appreciated by the researchers working in the field of fractional calculus and on fractional differential models.
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