scholarly journals Oscillation for a Class of Right Fractional Differential Equations on the Right Half Line with Damping

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Hui Liu ◽  
Run Xu
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Half Line ◽  
Riccati Transformation ◽  
Transformation Technique ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation ◽  
Fractional Differential ◽  
The Right

In this paper, we discuss a class of fractional differential equations of the form D-α+1y(t)·D-αy(t)-p(t)f(D-αy(t))+q(t)h∫t∞(s-t)-αy(s)ds=0.D-αy(t) is the Liouville right-sided fractional derivative of order α∈(0,1). We obtain some oscillation criteria for the equation by employing a generalized Riccati transformation technique. Some examples are given to illustrate the significance of our results.

scholarly journals The Oscillatory of Linear Conformable Fractional Differential Equations of Kamenev Type

2020 ◽  
Vol 2020 ◽  
pp. 1-8 ◽  
Author(s):  
Hui Liu ◽  
Run Xu
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Average Method ◽  
Riccati Transformation ◽  
Transformation Technique ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation ◽  
Fractional Differential ◽  
Integral Average

In this paper, the oscillatory of the Kamenev-type linear conformable fractional differential equations in the form of ptyα+1tα+yα+1t+qtyt=0 is studied, where t≥t0 and 0<α≤1. By employing a generalized Riccati transformation technique and integral average method, we obtain some oscillation criteria for the equation. We also give some examples to illustrate the significance of our results.

scholarly journals Oscillation for a Class of Fractional Differential Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Zhenlai Han ◽  
Yige Zhao ◽  
Ying Sun ◽  
Chao Zhang
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Real Number ◽  
Fractional Differential Equation ◽  
Riccati Transformation ◽  
Transformation Technique ◽  
Nonlinear Fractional Differential Equation ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation ◽  
Fractional Differential

We consider the oscillation for a class of fractional differential equation[r(t)g(D-αy)(t)]'-p(t)f∫t∞‍(s-t)-αy(s)ds=0,fort>0,where0<α<1is a real number andD-αyis the Liouville right-sided fractional derivative of orderαofy. By generalized Riccati transformation technique, oscillation criteria for a class of nonlinear fractional differential equation are obtained.

Comparison Principle and Solution Bound of Fractional Differential Equations

2015 ◽  
Author(s):  
Yufeng Xu
Keyword(s):  
Theoretical Analysis ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Numerical Simulations ◽  
Fractional Differential Equations ◽  
Comparison Principle ◽  
Lorenz System ◽  
Fractional Differential ◽  
Solution Bound ◽  
The Right

The comparison principle of fractional differential equations is discussed in this paper. We obtain two kinds of comparison principle which are related to the functions in the right hand side of equations, and the order of fractional derivative, respectively. By using the comparison principle, the boundedness of fractional Lorenz system and fractional Lorenz-like system are studied numerically. Numerical simulations are carried out which demonstrate our theoretical analysis.

scholarly journals Interval Oscillation Criteria for a Class of Fractional Differential Equations with Damping Term

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Chunxia Qi ◽  
Junmo Cheng
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Riccati Transformation ◽  
Damping Term ◽  
Oscillation Criteria ◽  
Interval Oscillation ◽  
Inequality Technique ◽  
Fractional Differential

Some new interval oscillation criteria are established based onthe certain Riccati transformation and inequality techniquefor a class of fractional differential equations with damping term. For illustrating the validity of the established results, we also present some applications for them.

scholarly journals Kamenev Type Oscillatory Criteria for Linear Conformable Fractional Differential Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Jing Shao ◽  
Zhaowen Zheng
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Average Method ◽  
Oscillation Theory ◽  
Conformable Fractional Derivative ◽  
Oscillation Criteria ◽  
Fractional Differential ◽  
Type Oscillation ◽  
Integral Average

Using integral average method and properties of conformable fractional derivative, new Kamenev type oscillation criteria are given firstly for conformable fractional differential equations, which improve known results in oscillation theory. Examples are also given to illustrate the effectiveness of the main results.

scholarly journals Hille and Nehari Type Oscillation Criteria for Conformable Fractional Differential Equations

2021 ◽  
pp. 578-587
Author(s):  
T. Gayathri ◽  
M. Sathish Kumar ◽  
V. Sadhasivam
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Conformable Fractional Derivative ◽  
Oscillation Criteria ◽  
All Solutions ◽  
Fractional Differential ◽  
Type Oscillation ◽  
Comparison Technique

In this paper, we develop the Hille and Nehari Type criteria for the oscillation of all solutions to the Fractional Differential Equations involving Conformable fractional derivative. Some new oscillatory criteria are obtained by using the Riccati transformations and comparison technique. We show the validity and effectiveness of our results by providing various examples.

scholarly journals Oscillation Behavior for a Class of Differential Equation with Fractional-Order Derivatives

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Shouxian Xiang ◽  
Zhenlai Han ◽  
Ping Zhao ◽  
Ying Sun
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Fractional Differential Equation ◽  
Fractional Order ◽  
Riccati Transformation ◽  
Transformation Technique ◽  
Generalized Riccati Transformation ◽  
Fractional Differential ◽  
Oscillation Theorems ◽  
Positive Integers

By using a generalized Riccati transformation technique and an inequality, we establish some oscillation theorems for the fractional differential equation[atpt+qtD-αxt)γ′ − b(t)f∫t∞‍(s-t)-αx(s)ds = 0, fort⩾t0>0, whereD-αxis the Liouville right-sided fractional derivative of orderα∈(0,1)ofxandγis a quotient of odd positive integers. The results in this paper extend and improve the results given in the literatures (Chen, 2012).

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