JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (4): 53-61.doi: 10.6040/j.issn.1671-9352.0.2022.565

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Existence and uniqueness of positive solutions of integral boundary value problems for a class of fractional differential equations with Hadamard derivatives

HU Fangfang1,2, HU Weimin1,2*, ZHANG Yong1,2   

  1. 1. College of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang, China;
    2. Institute of Applied Mathematics, Yili Normal University, Yining 835000, Xinjiang, China
  • Published:2024-04-12

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Abstract: A class of boundary value problems for Hadamard fractional differential equations with integral boundary value conditions is studied. The existence of positive solutions is obtained by Schauder fixed point theorem and the upper and lower solution method. The uniqueness result is obtained by Banach compression mapping principle, and an example is given to illustrate the effectiveness of the results.

Key words: Hadamard fractional derivative, fractional differential equation, fixed point theorem, existence and uniqueness

CLC Number: 

  • O175.14
[1] 杨小娟,韩晓玲. 一类带积分边值条件的分数阶微分方程多个正解的存在性[J]. 陕西师范大学学报(自然科学版),2017,45(6):1-4. YANG Xiaojuan, HAN Xiaoling. Multiplicity of positive solutions for a class of fractional differential equations with integral boundary value conditions[J]. Journal of Shaanxi Normal University(Natural Science Edition), 2017, 45(6):1-4.
[2] 张立新,杨玉洁,贾文敬. 一类Caputo分数阶微分方程积分边值问题的正解[J]. 四川大学学报(自然科学版),2017,54(6):1-4. ZHANG Lixin, YANG Yujie, JIA Wenjing. Positive solutions for integral boundary value problem of a class of Caputo fractional differential equations[J]. Journal of Sichuan University(Natural Science Edition), 2017, 54(6):1-4.
[3] MEHANDIRATTA V, MEHRA M, LEUGERING G. Existence and uniqueness results for a nonlinear Caputo fractional boundary value problem on a star graph[J]. Journal of Mathematical Analysis and Applications, 2019, 477(2):1243-1264.
[4] BOUIFOUI A, TEIIAB B, ABDEIIOUAHAB N, et al. Existence and uniqueness results for initial value problem of nonlinear fractional integro-differential equation on an unbounded domain in a weighted Banach space[J]. Mathematical Methods in the Applied Sciences, 2020, 44(5):3509-3520.
[5] AFSHARI H, JARAD F, ABDEIJAWAD T. On a new fixed point theorem with an application on a coupled system of fractional differential equations[J]. Advances in Difference Equations, 2020, 2020(461):4695-4706.
[6] NOURI K. Study on the existence and approximate solution of fractional differential equations with delay and its applications to financial models[J]. Journal of Pseudo-Differential Operators and Applications, 2021, 12(2):1-12.
[7] 董伟萍,周宗福. 一类分数阶微分方程多点边值问题正解的存在性(英文)[J]. 应用数学,2022,35(1):43-52. DONG Weiping, ZHOU Zongfu. Existence of positive solutions for a fractional differential equation with multi-point boundary value problems[J]. Mathematica Applicata, 2022, 35(1):43-52.
[8] LI Yating, LIU Yansheng. Multiple solutions for a class of boundary value problems of fractional differential equations with generalized Caputo derivatives[J]. AIMS Mathematics, 2021, 6(12):13119-13142.
[9] AGARWAL R, HRISTOVA S, OREGAN D. Explicit solutions of initial value problems for linear scalar Riemann-Liouville fractional differential equations with a constant delay[J]. Mathematics, 2019, 8(1):32-32.
[10] 杜听说,李成福. 具有Caputo-Hadamard导数的分数阶微分方程边值问题[J]. 应用数学,2020,33(4):964-971. DU Tingshuo, LI Chengfu. Boundary value problem of fractional differential equation with Caputo-Hadamard derivative[J]. Mathematica Applicata, 2020, 33(4):964-971.
[11] XU Mengrui, HAN Zhenlai. Positive solutions for integral boundary value problem of two-term fractional differential equations[J]. Bound Value Probl, 2018, 2018(100):1-13.
[12] KILBAS A A, SRIVASTAVA H M, TRUJILLO J J. Theory and applications of fractional differential equations[M]. Amsterdam: Elsevier, 2006(24):69-133.
[13] DEIMLING K. Nonlinear functional analysis[M]. Berlin: Springer, 1985:186-216.
[14] JIANG Daqing, GAO Wenjie. Upper and lower solution method and a singular boundary value problem for the one-dimensional p-Laplacian[J]. Journal of Mathematical Analysis and Applications, 2000, 252(2):631-648.
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