一类分数阶微分方程两点边值问题正解的存在性

doi:10.16088/j.issn.1001-6600.2017.04.010

Abstract

Abstract: In this paper, a class of two-point boundary value problem of fractional differential equations are studied:D^α₀₊u(t)=-f(t,u(t)), 0α≤3, D^α₀₊ is the standard Riemann-Liouville fractional derivative. The uniqueness of solution of the fractional two-point boundary value problem is acquired by using Banach’s contraction mapping principle, and the existence of positive solutions for the boundary value problem is obtained by using the fixed point index of the cohesive mapping under the general noncompactness measure condition.

Key words: fractional differential equation, Banach’s contraction principle, cohesive mapping, fixed point index

PANG Yang,WEI Yuming,FENG Chunhua. Existence of Positive Solutions for a Class of Two-point BoundaryValue Problem of Fractional Differential Equations[J].Journal of Guangxi Normal University(Natural Science Edition), 2017, 35(4): 68-75.

References

[1] BAI Zhanbing, L Haishen. Positive solutions for boundary value problem of nonlinear fractional differential equation[J]. Journal of Mathematical Analysis and Applications, 2005, 311(2): 495-505.DOI: 10.1016/j.jmaa.2005.02.052.
[2] KILBAS A A,SRIVASFAVA H M,TRUJILLO J J. Theory and applications of fractional differential equations[M]. Amsterdam: Elsevier Science,2006.
[3] NONNENMACHER T F, METZLER R. On the Riemann-Liouvile fractional calcules and some recent applications[J]. Fractals (Complex Geometry, Patterns, and Scaling in Nature and Society), 1995, 3(3): 557-566.DOI: 10.1142/S0218348X95000497.
[4] 张富平,周尚波,赵灿.基于分数阶偏微分方程的彩色图像去噪新方法[J].计算机应用研究,2013,30(3):946-949.DOI: 10.3969/j. issn.1001-3695.2013.03.079.
[5] BAI Zhanbing. On positive solutions of a nonlocal fractional boundary value problem[J].Nonlinear Analysis (Theory Methods and Applications),2010,72(2):916-924. DOI:10.1016/j.na.2009.07.033.
[6] 宋利梅,翁佩萱.四阶泛函微分方程边值问题正解的存在性[J].高校应用数学学报(A辑),2011,26(1):67-77.DOI:10.13299/j.cnki.amjcu.001631.
[7] 戴琛.一类分数阶积分多点边值问题正解的存在性[J].长春师范大学学报(自然科学版),2014,33(4):3-6.
[8] 陆心怡,张兴秋,王林.一类分数阶微分方程m点边值问题正解的存在性[J].系统科学与数学,2014,34(2):218-230.
[9] 秦丽娟.Banach空间中脉冲微分方程初值问题解的存在性[J].应用数学学报,2013,36(2):249-256.DOI:10.3969/j.issn.0254-3079.2013.02.007.
[10] 梁秋燕.有序Banach空间分数阶微分方程边值问题正解的存在性[J].河南师范大学学报(自然科学版),2014,42(1):16-20.DOI:10.16366/j.cnki.1000-2367.2014.01.004.
[11] LIANG Sihua, ZHANG Jihui.Existence of three positive solutions of m-point boundary value problems for some nonlinear fractional differential equations on an infinite interval[J].Computers and Mathematics with Applications,2011,61(11):3343-3354.DOI: 10.1016/j.camwa.2011.04.018.
[12] 郭大钧. 非线性泛函分析[M]. 北京: 高等教育出版社, 2015.
[13] 郭大钧,孙经先,刘兆理.非线性常微分方程泛函方法[M].济南:山东科学技术出版社,2006.
[14] 李永祥.抽象半线性发展方程初值问题解的存在性[J].数学学报,2005,48(6):1089-1094.DOI:10.3321/j.issn:0583-1431.2005.06.006.
[15] 郭大钧,孙经先.抽象空间常微分方程[M].济南:山东科学技术出版社,1998.
[16] HEINZ H P. On the behaviour of measures of noncompactness with respect to differentiation and integration of vector-valued functions[J].Nonlinear Analysis (Theory, Methods and Applications),1983,7(12):1351-1371.DOI: 10.1016/0362-546X(83)90006-8.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed

Comments

Recommended 0

No Suggested Reading articles found!

Existence of Positive Solutions for a Class of Two-point BoundaryValue Problem of Fractional Differential Equations

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 3

Metrics

Comments

Recommended 0

[1]	ZHU Yaping, QU Guorong, FAN Jianghua. The Existence of Solutions for Quasi-variational Inequalities by Using the Fixed Point Index Approach [J]. Journal of Guangxi Normal University(Natural Science Edition), 2019, 37(4): 79-85.
[2]	HUANG Yanping, WEI Yuming. Multiple Solutions of Multiple-points Boundary Value Problem for a Class of Fractional Differential Equation [J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(3): 41-49.
[3]	YAN Rongjun, WEI Yuming, FENG Chunhua. Existence of Three Positive Solutions for Fractional Differential Equation ofBoundary Value Problem with p-Laplacian Operator and Delay [J]. Journal of Guangxi Normal University(Natural Science Edition), 2017, 35(3): 75-82.