一类Caputo分数阶脉冲微分方程混合边值问题解的存在唯一性
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摘要
主要研究了一类1<α<2的分数阶脉冲微分方程的混合边值问题.首先将非线性微分方程转化为等价的积分方程,然后利用Leray-Schauder和Altman不动点定理,得到了解的存在性和唯一性,并且给出了一个例子说明结论的正确性,推广和改进了相关结论.
In this paper, we study a class of Caputo fractional impulsive differential equations with the mixed boundary value problem of fractional order α∈(1, 2). Firstly, we transform the non-linear differential equation into an equivalent fractional integral equation. Secondly, by using the Leray-Schauder and Altman fixed point theorem, we obtain the existence and uniqueness of the solution. Finally, an example is given to demonstrate the validity of the main result, and relevant results are generalized and improved.
In this paper, we study a class of Caputo fractional impulsive differential equations with the mixed boundary value problem of fractional order α∈(1, 2). Firstly, we transform the non-linear differential equation into an equivalent fractional integral equation. Secondly, by using the Leray-Schauder and Altman fixed point theorem, we obtain the existence and uniqueness of the solution. Finally, an example is given to demonstrate the validity of the main result, and relevant results are generalized and improved.
引文
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[2] XING Y Y,YAN Y B.A Higher Order Numerical Method for Time Fractional Partial Differential Equations with Nonsmooth Data [J].Journal of Computational Physics,2018,357:305-323.
[3] 罗丽容,周军.一类带有分数型交错扩散的捕食-食饵模型的多解性研究 [J].西南大学学报(自然科学版),2017,39(3):108-114.
[4] DELBOSCO D,RODINO L.Existence and Uniqueness for a Nonlinear Fractional Differential Equation [J].Journal of Mathematical Analysis & Applications,1996,204(2):609-625.
[5] BAYOUR B,TORRES D F M.Existence of Solution to a Local Fractional Nonlinear Differential Equation [J].Journal of Computational and Applied Mathematics,2017,312:127-133.
[6] 郭彩霞,郭建敏,田海燕,等.一类分数阶奇异q-差分方程边值问题解的存在性和唯一性 [J].西南师范大学学报(自然科学版),2018,43(12):6-10.
[7] MAHMUDOV N,UNUL S.On Existence of BVP's for Impulsive Fractional Differential Equations [J].Advances in Difference Equations,2017,2017:15.
[8] BENCHOHRA M,HENDERSON J,NTOUYAS S.Impulsive Differential Equations and Inclusions [M].New York:Hindawi Publishing Corporation,2006.
[9] SAMOILENKO A M,PERESTYUK N A.Impulsive Differential Equations [M].Singapore:World Scientific,1995.
[10] WANG S A.The Existence of Affine-Periodic Solutions for Nonlinear Impulsive Differential Equations [J].Boundary Value Problems,2018,2018(1):113.
[11] HU Y X,LI F.Existence of Solutions for the Nonlinear Multiple Base Points Impulsive Fractional Differential Equations with the Three-Point Boundary Conditions [J].Advances in Difference Equations,2017,2017(1):55.
[12] WANG Q,WEI T Y.On the Natural Solution of Generalized Anti-periodic BVP of Impulsive Fractional Differential Equations [J].Mathematic Applicata,2017,30(1):78-89.
[13] BAI Z B,DONG X Y,YIN C.Existence Results for Impulsive Nonlinear Fractional Differential Equation with Mixed Boundary Conditions [J].Boundary Value Problems,2016,2016(1):63.
[14] KILBAS A A,SRIVASTAVA H M,TRUJILLO J J.Theory and Applications of Fractional Differential Equations [M].Amsterdam:Elsevier,2006.
[15] 张恭庆,林源渠.泛函分析讲义(上册) [M].北京:北京大学出版社,2006.
[16] 郭大钧.非线性泛函分析 [M].3版.北京:高等教育出版社,2015.
[2] XING Y Y,YAN Y B.A Higher Order Numerical Method for Time Fractional Partial Differential Equations with Nonsmooth Data [J].Journal of Computational Physics,2018,357:305-323.
[3] 罗丽容,周军.一类带有分数型交错扩散的捕食-食饵模型的多解性研究 [J].西南大学学报(自然科学版),2017,39(3):108-114.
[4] DELBOSCO D,RODINO L.Existence and Uniqueness for a Nonlinear Fractional Differential Equation [J].Journal of Mathematical Analysis & Applications,1996,204(2):609-625.
[5] BAYOUR B,TORRES D F M.Existence of Solution to a Local Fractional Nonlinear Differential Equation [J].Journal of Computational and Applied Mathematics,2017,312:127-133.
[6] 郭彩霞,郭建敏,田海燕,等.一类分数阶奇异q-差分方程边值问题解的存在性和唯一性 [J].西南师范大学学报(自然科学版),2018,43(12):6-10.
[7] MAHMUDOV N,UNUL S.On Existence of BVP's for Impulsive Fractional Differential Equations [J].Advances in Difference Equations,2017,2017:15.
[8] BENCHOHRA M,HENDERSON J,NTOUYAS S.Impulsive Differential Equations and Inclusions [M].New York:Hindawi Publishing Corporation,2006.
[9] SAMOILENKO A M,PERESTYUK N A.Impulsive Differential Equations [M].Singapore:World Scientific,1995.
[10] WANG S A.The Existence of Affine-Periodic Solutions for Nonlinear Impulsive Differential Equations [J].Boundary Value Problems,2018,2018(1):113.
[11] HU Y X,LI F.Existence of Solutions for the Nonlinear Multiple Base Points Impulsive Fractional Differential Equations with the Three-Point Boundary Conditions [J].Advances in Difference Equations,2017,2017(1):55.
[12] WANG Q,WEI T Y.On the Natural Solution of Generalized Anti-periodic BVP of Impulsive Fractional Differential Equations [J].Mathematic Applicata,2017,30(1):78-89.
[13] BAI Z B,DONG X Y,YIN C.Existence Results for Impulsive Nonlinear Fractional Differential Equation with Mixed Boundary Conditions [J].Boundary Value Problems,2016,2016(1):63.
[14] KILBAS A A,SRIVASTAVA H M,TRUJILLO J J.Theory and Applications of Fractional Differential Equations [M].Amsterdam:Elsevier,2006.
[15] 张恭庆,林源渠.泛函分析讲义(上册) [M].北京:北京大学出版社,2006.
[16] 郭大钧.非线性泛函分析 [M].3版.北京:高等教育出版社,2015.