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

Abstract

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_0

Keywords

• mixed-compound equation
• fractional derivative
• difference operator
• tricomi problem