On the oscillation of fractional Emden–Fowler type neutral partial differential equations

Abstract

In this paper, we consider a new class of boundary value problem associated with fractional Emden–Fowler type neutral partial differential equations of the form

$$ \begin{gathered} D_{{ + ,t}}^{\alpha } \left[ {r(t)D_{{ + ,t}}^{\alpha } \left( {u(x,t) + p(t)u(x,t - \tau )} \right)} \right] + q(x,t)\left| {u(x,\sigma (t))} \right|^{{\gamma - 1}} u(x,\sigma (t)) \hfill \\ = a(t)\Delta u(x,t) + F(x,t),~~(x,t) \in \Omega \times \mathbb{R}_{ + } = G,{\text{ }} \hfill \\ \end{gathered} $$

$\int \nolimits _{t_0}^{\infty }\dfrac{dt}{r(t)}<\infty$. We will establish the sufficient conditions for the oscillation of given system by using the generalized Riccati technique and integral averaging method.