Forced oscillation of a certain system of fractional partial differential equations

2021 ◽  
Vol 10 (4) ◽  
pp. 607-615
Author(s):  
R. Ramesh ◽  
P. Prakash ◽  
S. Harikrishnan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Forced Oscillation ◽  
Fractional Partial Differential Equations ◽  
Partial Differential

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.

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.

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