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

Abstract EN

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+ or u(x,t)=0, (x,t)∈∂Ω×R+, where Ω is a bounded domain in Rn with a piecewise smooth boundary, ∂Ω,R+=[0,∞), α∈(0,1) is a constant, D+,tαu(x,t) is the Riemann-Liouville fractional derivative of order α of u with respect to t, Δ is the Laplacian in Rn, N is the unit exterior normal vector to ∂Ω, and ψ(x,t) is a continuous function on ∂Ω×R+.

The main results are illustrated by some examples.