scholarly journals Some New Oscillation Criteria for a Class of Nonlinear Fractional Differential Equations with Damping Term

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Bin Zheng ◽  
Qinghua Feng
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Damping Term ◽  
Oscillation Criteria ◽  
Nonlinear Fractional Differential Equations ◽  
Inequality Technique ◽  
Fractional Differential ◽  
Oscillation Of Solutions

We are concerned with oscillation of solutions of a class of nonlinear fractional differential equations with damping term. Based on a generalized Riccati function and inequality technique, we establish some new oscillation criteria for it. Some applications are also presented for the established 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.

On the oscillation of fractional differential equations

2012 ◽  
Vol 15 (2) ◽  
Author(s):  
Said Grace ◽  
Ravi Agarwal ◽  
Patricia Wong ◽  
Ağacık Zafer
Keyword(s):  
Differential Operator ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Oscillation Theory ◽  
Oscillation Criteria ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential

AbstractIn 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),\mathop {\lim }\limits_{t \to a} J_a^{1 - q} x(t) = b_1 $, where D aq 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.

scholarly journals Implicit nonlinear fractional differential equations of variable order

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Amar Benkerrouche ◽  
Mohammed Said Souid ◽  
Kanokwan Sitthithakerngkiet ◽  
Ali Hakem
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Variable Order ◽  
Stability Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
The Stability

AbstractIn this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order. We construct an example to illustrate the validity of the observed results.

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