scholarly journals Interval Oscillation Criteria for Fractional Partial Differential Equations with Damping Term

2016 ◽  
Vol 07 (03) ◽  
pp. 272-291
Author(s):  
Vadivel Sadhasivam ◽  
Jayapal Kavitha
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Partial Differential Equations ◽  
Damping Term ◽  
Partial Differential ◽  
Oscillation Criteria ◽  
Interval Oscillation

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 Interval oscillation criteria for impulsive conformable partial differential equations

2019 ◽  
Vol 13 (1) ◽  
pp. 325-345
Author(s):  
G.E. Chatzarakis ◽  
K. Logaarasi ◽  
T. Raja ◽  
V. Sadhasivam
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Qualitative Properties ◽  
Partial Differential ◽  
Oscillation Criteria ◽  
All Solutions ◽  
Two Factors ◽  
Interval Oscillation ◽  
Impulsive Delay

In this paper, we present some sufficient conditions for the oscillation of all solutions of forced impulsive delay conformable partial differential equations. We consider two factors, namely impulse and delay that jointly affect the interval qualitative properties of the solutions of those equations. The results obtained in this paper extend and generalize some of the known results for forced impulsive conformable partial differential equations. An example illustrating the results is also given.

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

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Wei Nian Li
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Forced Oscillation ◽  
Smooth Boundary ◽  
Sufficient Conditions ◽  
Normal Vector ◽  
Fractional Partial Differential Equations ◽  
Damping Term ◽  
Partial Differential ◽  
Liouville Fractional Derivative

Sufficient conditions are established for the forced oscillation of fractional partial differential equations with damping term of the form(∂/∂t)(D+,tαu(x,t))+p(t)D+,tαu(x,t)=a(t)Δu(x,t)-q(x,t)u(x,t)+f(x,t),(x,t)∈Ω×R+≡G, with one of the two following boundary conditions:∂u(x,t)/∂N=ψ(x,t),  (x,t)∈∂Ω×R+oru(x,t)=0,  (x,t)∈∂Ω×R+, whereΩis a bounded domain inRnwith a piecewise smooth boundary,∂Ω,R+=[0,∞),  α∈(0,1)is a constant,D+,tαu(x,t)is the Riemann-Liouville fractional derivative of orderαofuwith respect tot,Δis the Laplacian inRn,Nis the unit exterior normal vector to∂Ω, andψ(x,t)is a continuous function on∂Ω×R+. The main results are illustrated by some examples.

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