In the domain D= ∪ +∞ k=0 Dk, Dk={(x,y):0＜x＜τ,kh＜y≤(k+1)h} (0＜h, τ≡ const), we consider the following diffusion equation with fractional derivative and with distributed time delay: Dα 0y u (x,t)-uxx(x,y)=∫h 0 R(ξ)u(x,y-ξ)dξ, 0＜α＜1, where Dα 0y is the Riemann-Liouville fractional integro-differentiation operator [1, p., 43] acting on the function u(x, y) with respect to the variable y and R(ξ) is a given bounded function.
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