Interval Oscillation Criteria for a Class of Nonlinear Fractional Differential Equations with Nonlinear Damping Term
نویسنده
چکیده
In this paper, based on certain variable transformation, we apply the known (G’/G) method to seek exact solutions for three fractional partial differential equations: the space fractional (2+1)-dimensional breaking soliton equations, the space-time fractional Fokas equation, and the spacetime fractional Kaup-Kupershmidt equation. The fractional derivative is defined in the sense of modified Riemann-liouville derivative. With the aid of mathematical software Maple, a number of exact solutions including hyperbolic function solutions, trigonometric function solutions, and rational function solutions for them are obtained.
منابع مشابه
Interval Oscillation of a Second Order Nonlinear Differential Equation with a Damping Term
Using generalized Riccati transformations, we derive new interval oscillation criteria for a class of second order nonlinear differential equations with damping. Our theorems prove to be efficient in many cases where known results fail to apply.
متن کاملInterval Oscillation Criteria For A Class Of Nonlinear Fractional Differential Equations
In this work, some new interval oscillation criteria for solutions of a class of nonlinear fractional differential equations are established by using a generalized Riccati function and inequality technique. For illustrating the validity of the established results, we also present some applications for them. Key–Words: Oscillation; Interval criteria; Qualitative properties; Fractional differenti...
متن کاملOscillation criteria for second-order nonlinear differential equations with nonlinear damping
Using generalized Riccati transformations, we derive new interval oscillation criteria for a class of general type second-order nonlinear differential equations with nonlinear damping. Examples are also given to illustrate the results. 2000 Mathematics Subject Classification: 34C10
متن کاملSome New Oscillation Criteria for a Class of Nonlinear Fractional Differential Equations with Damping Term
Several oscillation criteria are established for nonlinear fractional differential equations of the form{ a(t) [( r(t)g ( D−x(t) ))′]η}′ −F(t,∫ ∞ t (v− t)−αx(v)dv ) = 0, where D−x(t) is the Liouville right-side fractional derivative of order α ∈ (0,1) of x(t),η = 2n+1 2m+1 , and n,m∈N . F(t,G)∈C([t0,∞)×R;R) , and there exists function q(t)∈ C([t0,∞);R+) such that F(t,G) Gη q(t) for G = 0 and x ...
متن کاملOscillation Criteria for Second-order Nonlinear Differential Equations with Damping Term
By employing a generalized Riccati technique and an integral averaging technique, new oscillation criteria are established for a class of second-order nonlinear differential equations with damping term. These criteria extend, improve and unify a number of existing results and handle the cases which are not covered by the known criteria. In particular, several interesting examples that illustrat...
متن کامل