GAN Yimiao,HOU Chengmin*.The existence and uniqueness of the solutions of a class ofHilfer fractional differential equations[J].Journal of Yanbian University,2020,46(02):95-100.
一类Hilfer型分数阶微分方程解的存在和唯一性
- Title:
- The existence and uniqueness of the solutions of a class of Hilfer fractional differential equations
- 文章编号:
- 1004-4353(2020)02-0095-06
- 关键词:
- Hilfer分数阶微分方程; 上下解方法; Banach不动点定理; 唯一性
- Keywords:
- Hilfer fractional differential equation; upper and lower solution methods; Banach fixed point theorem; uniqueness
- 分类号:
- O175.6
- 文献标志码:
- A
- 摘要:
- 用Banach不动点定理和上下解方法研究了α(1<α <2)阶数和β(0≤β ≤1)类型Hilfer分数阶微分方程的解,给出了方程解的存在和唯一性,并通过例证验证了本文所得结果的有效性.
- Abstract:
- The Banach fixed point theorem and upper and lower solution methods are used to study the solutions of the order α(1<α <2)and type β(0≤β ≤1)of Hilfer fractional differential equations. The existence and uniqueness of the solutions of the equations are given. The validity of the results obtained in this paper is proved by examples.
参考文献/References:
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[2] FURATI K M, KASSIM M D. Existence and uniqueness for a problem involving Hilfer fractional derivative[J]. Computers and Mathematics at with Applications, 2012,64(6):1616-1626.
[3] ANAJALI J, BAHUGUNA D. Existence and regularity of solutions of fractional differential equations involving Hilfer fractional derivative of order 1<α<2 and type 0≤β≤1[OL].[2019-07-26].https://arxiv.org/.
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[8] SHU X B, WANG Q Q. The existence and uniqueness of mild solutions for fractional differential equations with nonlocal conditions of order 1<α<2 [J]. Computers and Mathematics with Applications, 2012,2012(64):2100-2110.
[9] LIN L G, LIU X P, FANG H Q. Method of upper and lower solutions for fractional differential equations[J]. Electronic Journal of Differential Equations, 2012,2012(100):1-13.
[10] ABBAS S, BENCHOHRA M, ZHOU Y. Couple Hilfer fractional differential systems with random effects[J]. Advances in Difference Equations, 2018,2018:369-380.
相似文献/References:
[1]苏巍,刘畅,李丹,等.一类分数阶q -差分方程边值问题正解的存在性[J].延边大学学报(自然科学版),2015,41(02):103.
SU Wei,LIU Chang,LI Dan,et al.Existence of positive solutions for a class of the boundary value problems of fractional q-difference equations[J].Journal of Yanbian University,2015,41(02):103.
备注/Memo
收稿日期: 2020-04-15
*通信作者: 侯成敏(1963—),女,教授,研究方向为微分理论及其应用.