On the oscillation of fractional differential equations

被引：107

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

[31] Oscillation Tests for Conformable Fractional Differential Equations with Damping [J].

Ladrani, Fatima Zohra ;

Cherif, Amine Benaissa .

PUNJAB UNIVERSITY JOURNAL OF MATHEMATICS, 2020, 52 (02) :73-82

[32] Oscillation criteria of certain fractional partial differential equations [J].

Xu, Di ;

Meng, Fanwei .

ADVANCES IN DIFFERENCE EQUATIONS, 2019, 2019 (01)

[33] Oscillation theorems for three classes of conformable fractional differential equations [J].

Limei Feng ;

Shurong Sun .

Advances in Difference Equations, 2019

[34] INTERVAL OSCILLATION CRITERIA FOR IMPULSIVE CONFORMABLE FRACTIONAL DIFFERENTIAL EQUATIONS [J].

Bolat, Yasar ;

Raja, Thangaraj ;

Logaarasi, Kandhasamy ;

Sadhasivam, Vadivel .

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, 2020, 69 (01) :815-831

[35] On the oscillation of differential equations in frame of generalized proportional fractional derivatives [J].

Sudsutad, Weerawat ;

Alzabut, Jehad ;

Tearnbucha, Chutarat ;

Thaiprayoon, Chatthai .

AIMS MATHEMATICS, 2020, 5 (02) :856-871

[36] Oscillation of fractional order functional differential equations with nonlinear damping [J].

Bayram, Mustafa ;

Adiguzel, Hakan ;

Ogrekci, Suleyman .

OPEN PHYSICS, 2015, 13 (01) :377-382

[37] Oscillation theorems for three classes of conformable fractional differential equations [J].

Feng, Limei ;

Sun, Shurong .

ADVANCES IN DIFFERENCE EQUATIONS, 2019, 2019 (01)

[38] Interval oscillation criteria for functional differential equations of fractional order [J].

Ogrekci, Suleyman .

ADVANCES IN DIFFERENCE EQUATIONS, 2015,

[39] New criteria for oscillation of damped fractional partial differential equations [J].

Luo, Zhenguo ;

Luo, Liping .

MATHEMATICAL MODELLING AND CONTROL, 2022, 2 (04) :219-227

[40] Forced Oscillation of a Certain System of Fractional Partial Differential Equations [J].

Ramesh, R. ;

Prakash, P. ;

Harikrishnan, S. .

JOURNAL OF APPLIED NONLINEAR DYNAMICS, 2021, 10 (04) :607-615

← 1 2 3 4 5 →