JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (12): 40-44.doi: 10.6040/j.issn.1671-9352.0.2021.145
LUO Li-ping, ZENG Yun-hui, LUO Zhen-guo
CLC Number:
| [1] PODLUBNY I. Fractional differential equations[M]. San Diego: Academic Press, 1999. [2] KILBAS A A, SRIVASTAVA H M, TRUJILLO J J. Theory and applications of fractional differential equations[M]. Amsterdam: Elsevier B V, 2006. [3] DAS S. Functional fractional calculus for system identification and controls[M]. New York: Springer, 2008. [4] ABBAS S, BENCHOHRA M, NGUÉRÉKATA G M. Topics in fractional differential equations[M]. New York: Springer, 2012. [5] ZHOU Yong, WANG Jinrong, ZHANG Lu. Basic theory of fractional differential equations[M]. 2nd ed. Singapore: World Scientific Publishing Co Pte Ltd, 2016. [6] GRACE S R, AGARWAL R P, WONG P J Y, et al. On the oscillation of fractional differential equations[J]. Fractional Calculus and Applied Analysis, 2012,15(2):222-231. [7] CHEN Daxue. Oscillatory behavior of a class of fractional differential equations with damping[J]. U P B Sci Bull, Series A, 2013, 75(1):107-118. [8] FENG Qinghua, MENG Fanwei. Oscillation of solutions to nonlinear forced fractional differential equations[J]. Electronic Journal of Differential Equations, 2013(169):1-10. [9] BOLAT Y. On the oscillation of fractional-order delay differential equations with constant coefficients[J]. Communications in Nonlinear Science & Numerical Simulations, 2014, 19(11):3988-3993. [10] YANG Jichen, LIU Anping, LIU Ting. Forced oscillation of nonlinear fractional differential equations with damping term[J]. Advances in Difference Equations, 2015(1):1-7. [11] TUNÇ E, TUNÇ O. On the oscillation of a class of damped fractional differential equations[J]. Miskolc Mathematical Notes, 2016, 17(1):647-656. [12] APHITHANA A, NTOUYAS S K, TARIBOON J. Forced oscillation of fractional differential equations via conformable derivatives with damping term[J]. Boundary Value Problems, 2019(1):1-16. [13] FENG Limei, SUN Shurong. Oscillation theorems for three classes of conformable fractional differential equations[J]. Advances in Difference Equations, 2019(1):1-30. [14] SUN Yufeng, ZENG Zheng, SONG Jie. Quasilinear iterative method for the boundary value problem of nonlinear fractional differential equation[J]. Numerical Algebra, 2019, 10(2):157-164. [15] PRAKASH P, HARIKRISHNAN S, NIETO J J, et al. Oscillation of a time fractional partial differential equation[J]. Electronic Journal of Qualitative Theory of Differential Equations, 2014(15):1-10. |
| [1] | CAO Xue-qin, GAO Cheng-hua. Spectrum of a class of discrete left-definite Sturm-Liouville problems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(9): 42-49. |
| [2] | WANG Min, FANG Xiao-zhen, QU Meng, SHU Li-sheng. Boundedness for commutator of multilinear Hardy-Littlewood maximal operator [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(2): 16-22. |
| [3] | SONG Jun-qiu, JIA Mei, LIU Xi-ping, LI Lin. Existence of positive solutions for fractional nonhomogeneous boundary value problem with p-Laplacian [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(10): 57-66. |
| [4] | DONG Li. Lower bounds for blow up time of two nonlinear wave equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(4): 56-60. |
| [5] | ZHANG Sha, JIA Mei, LI Yan, LI Xiao-chen. Existence and uniqueness of solutions for three point boundary value problems of impulsive fractional differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 66-72. |
| [6] | ZHANG Di, LIU Wen-bin. Existence of solutions for p(t)-Laplacian fractional infinite-point boundary value problems at resonance [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 72-80. |
| [7] | SU Xiao-feng, JIA Mei, LI Meng-meng. Existence of solution for fractional differential equation integral boundary value problem at resonance [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(8): 66-73. |
| [8] | LUO Li-ping, LUO Zhen-guo, ZENG Yun-hui. (Full)oscillatory problems of certain quasilinear hyperbolic systems with damping term [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(6): 73-77. |
| [9] | ZHONG Qiu-yan, ZHANG Xing-qiu. Positive solutions for some singular fractional differential equation integral boundary value problems with p-Laplacian and a parameter [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(6): 78-84. |
| [10] | YANG Hao, LIU Xi-ping, WU Gui-yun. Existence of the solutions for a type of nonlocal boundary value problems for fractional differential equations with p-Laplacian operator [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(04): 56-62. |
| [11] | LUO Li-ping, LUO Zhen-guo, ZENG Yun-hui. (Strong) oscillation analysis of quasilinear hyperbolic systems with impulse effect [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(03): 57-61. |
| [12] | CHEN Yi-ming, KE Xiao-hong, HAN Xiao-ning, SUN Yan-nan, LIU Li-qing. Wavelets method for solving system of fractional differential equations and the convergence analysis [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(02): 67-74. |
| [13] | ZHOU Wen-xue1,2, LIU Hai-zhong1. Existence of solution for the boundary value problem of a class of fractional differential equation [J]. J4, 2013, 48(8): 45-49. |
| [14] | GAO Zheng-hui, LUO Li-ping. Philos-type oscillation criteria for third-order nonlinear functional differential equations with distributed delays and damped terms [J]. J4, 2013, 48(4): 85-90. |
| [15] |
LI Fan-fan, LIU Xi-ping*, ZHI Er-tao.
Existence of a solution for the boundary value problem of fractional differential equation with delay [J]. J4, 2013, 48(12): 24-29. |
|
||
