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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Fangfang HU1,2(),Weimin HU1,2,*(),Yong ZHANG1,2
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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.
doi: 10.1016/j.jmaa.2019.05.011 |
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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