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 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 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 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 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.

scholarly journals Oscillation criteria for half-linear function differential equations with damping

2014 ◽  
Vol 18 (5) ◽  
pp. 1537-1542 ◽  
Author(s):  
Jun Liu ◽  
Hong-Ying Luo ◽  
Xi Liu
Keyword(s):  
Differential Equations ◽  
Linear Function ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Riccati Transformation ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation ◽  
Functional Differential ◽  
Integral Average

In this paper, a class of half-linear functional differential equations with damping are studied. By using the generalized Riccati transformation and integral average skills, new oscillation criteria are obtained which generalize and improve some known results.

scholarly journals Oscillation criteria of certain fractional partial differential equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Di Xu ◽  
Fanwei Meng
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Derivatives ◽  
Sufficient Conditions ◽  
Riccati Transformation ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation

Abstract In this article, we regard the generalized Riccati transformation and Riemann–Liouville fractional derivatives as the principal instrument. In the proof, we take advantage of the fractional derivatives technique with the addition of interval segmentation techniques, which enlarge the manners to demonstrate the sufficient conditions for oscillation criteria of certain fractional partial differential equations.

scholarly journals Oscillatory Behavior of a Type of Generalized Proportional Fractional Differential Equations with Forcing and Damping Terms

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1037 ◽  
Author(s):  
Jehad Alzabut ◽  
James Viji ◽  
Velu Muthulakshmi ◽  
Weerawat Sudsutad
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Oscillatory Behavior ◽  
Numerical Examples ◽  
Oscillation Criteria ◽  
Fractional Differential

In this paper, we study the oscillatory behavior of solutions for a type of generalized proportional fractional differential equations with forcing and damping terms. Several oscillation criteria are established for the proposed equations in terms of Riemann-Liouville and Caputo settings. The results of this paper generalize some existing theorems in the literature. Indeed, it is shown that for particular choices of parameters, the obtained conditions in this paper reduce our theorems to some known results. Numerical examples are constructed to demonstrate the effectiveness of the our main theorems. Furthermore, we present and illustrate an example which does not satisfy the assumptions of our theorem and whose solution demonstrates nonoscillatory behavior.

scholarly journals Oscillation criteria for nonlinear fractional differential equation with damping term

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 119-128 ◽  
Author(s):  
Mustafa Bayram ◽  
Hakan Adiguzel ◽  
Aydin Secer
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Riccati Transformation ◽  
Damping Term ◽  
Nonlinear Fractional Differential Equation ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation ◽  
Liouville Derivative ◽  
Fractional Differential ◽  
Oscillation Of Solutions

AbstractIn this paper, we study the oscillation of solutions to a non-linear fractional differential equation with damping term. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. By using a variable transformation, a generalized Riccati transformation, inequalities, and integration average techniquewe establish new oscillation criteria for the fractional differential equation. Several illustrative examples are also given.

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

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Huizeng Qin ◽  
Bin Zheng
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Riccati Transformation ◽  
Damping Term ◽  
Variable Transformation ◽  
Average Technique ◽  
Integer Order ◽  
Fractional Differential

We investigate the oscillation of a class of fractional differential equations with damping term. Based on a certain variable transformation, the fractional differential equations are converted into another differential equations of integer order with respect to the new variable. Then, using Riccati transformation, inequality, and integration average technique, some new oscillatory criteria for the equations are established. As for applications, oscillation for two certain fractional differential equations with damping term is investigated by the use of the presented results.

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