| 一类含高阶Riemann-Liouville型分数阶导数脉冲微分方程的通解 |
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| 引用本文： | 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. |
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| 作者姓名： | 刘玉记 |
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| 作者单位： | 广东财经大学数学与统计学院, 广东 广州 510320 |
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| 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). |
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| 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.
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| 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 |
| 收稿时间： | 2018/12/3 0:00:00 |
| 修稿时间： | 2019/9/3 0:00:00 |
General Solutions of a Higher Order Impulsive Fractional Differential Equation Involving the Riemann-Liouville Fractional Derivatives |
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| Yuji LIU.General Solutions of a Higher Order Impulsive Fractional Differential Equation Involving the Riemann-Liouville Fractional Derivatives[J].Journal of Mathematical Research with Applications,2020,40(2):140-164. |
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| Authors: | Yuji LIU |
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| Institution: | Department of Mathematics, Guangdong University of Finance and Economics, Guangdong 510000, P. R. China |
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| Abstract: | 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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| Keywords: | higher order fractional differential equation piecewise continuous solution Riemann-Liouville fractional derivative impulse effect |
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