On the oscillation of fractional differential equations

被引：101

作者：

Grace, Said R. ^{[1
]}

Agarwal, Ravi P. ^{[2
]}

Wong, Patricia J. Y. ^{[3
]}

Zafer, Agacik ^{[4
]}

机构：

[1] Cairo Univ, Fac Engn, Dept Engn Math, Giza 12221, Egypt

[2] Texas A&M Univ, Dept Math, Kingsville, TX 78363 USA

[3] Nanyang Technol Univ, Sch Elect & Elect Engn, Singapore 639798, Singapore

[4] Middle E Tech Univ, Dept Math, TR-06800 Ankara, Turkey

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2012年 / 15卷 / 02期

关键词：

fractional differential equation; oscillation; Riemann-Liouville operators; Caputo derivative;

D O I：

10.2478/s13540-012-0016-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we initiate the oscillation theory for fractional differential equations. Oscillation criteria are obtained for a class of nonlinear fractional differential equations of the form D(a)(q)x + f(1)(t, x) = v(t) + f(2)(t, x), lim(t -> a+) J(a)(1-q)x(t)= b(1), where D-a(q) denotes the Riemann-Liouville differential operator of order q, 0 < q <= 1. The results are also stated when the Riemann-Liouville differential operator is replaced by Caputo's differential operator.

引用

页码：222 / 231

页数：10

共 50 条

[1] On the oscillation of fractional differential equations
Said R. Grace
Ravi P. Agarwal
Patricia J.Y. Wong
Ağacık Zafer
Fractional Calculus and Applied Analysis, 2012, 15 : 222 - 231
[2] Oscillation for Fractional Partial Differential Equations
Zhou, Yong
Ahmad, Bashir
Chen, Fulai
Alsaedi, Ahmed
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2019, 42 (02) : 449 - 465
[3] On the oscillation of Hadamard fractional differential equations
Abdalla, Bahaaeldin
Abdeljawad, Thabet
ADVANCES IN DIFFERENCE EQUATIONS, 2018,
[4] Oscillation for Fractional Partial Differential Equations
Yong Zhou
Bashir Ahmad
Fulai Chen
Ahmed Alsaedi
Bulletin of the Malaysian Mathematical Sciences Society, 2019, 42 : 449 - 465
[5] Oscillation criteria of fractional differential equations
Da-Xue Chen
Advances in Difference Equations, 2012
[6] On the oscillation of Hadamard fractional differential equations
Bahaaeldin Abdalla
Thabet Abdeljawad
Advances in Difference Equations, 2018
[7] Oscillation criteria of fractional differential equations
Chen, Da-Xue
ADVANCES IN DIFFERENCE EQUATIONS, 2012, : 1 - 10
[8] ON THE OSCILLATION OF A CLASS OF DAMPED FRACTIONAL DIFFERENTIAL EQUATIONS
Tunc, Ercan
Tunc, Osman
MISKOLC MATHEMATICAL NOTES, 2016, 17 (01) : 647 - 656
[9] Oscillation Criteria for Nonlinear Fractional Differential Equations
Xu, Run
JOURNAL OF APPLIED MATHEMATICS, 2013,
[10] Oscillation on a Class of Differential Equations of Fractional Order
Liu, Tongbo
Zheng, Bin
Meng, Fanwei
MATHEMATICAL PROBLEMS IN ENGINEERING, 2013, 2013

← 1 2 3 4 5 →