Boundary value problem for mixed-compound equation with fractional derivative, functional delay and advance

We study the Tricomi problem for the functional-differential mixed-compound equation $LQu(x,y)=0$ in the class of twice continuously differentiable solutions. Here $L$ is a differential-difference operator of mixed parabolic-elliptic type with Riemann–Liouville fractional derivative and linear shift by $y$. The $Q$ operator includes multiple functional delays and advances $a_1(x)$ and $a_2(x)$ by $x$. The functional shifts $a_1(x)$ and $a_2(x)$ are the orientation preserving mutually inverse diffeomorphisms. The integration domain is $D=D^+\cup D^-\cup I$. The “parabolicity” domain $D^+$ is the set of $(x,y)$ such that $x_00$. The ellipticity domain is $D^-=D_0^-\cup D_1^-\cup D_2^-$, where $D_k^-$ is the set of $(x,y)$ such that $x_k

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