An analog of the Tricomi problem for a mixed type equation with Riemann-Liouville fractional derivative

TL;DR

This paper investigates a Tricomi problem for a mixed parabolic-hyperbolic equation involving Riemann-Liouville fractional derivatives, addressing the mathematical challenges of fractional calculus in mixed-type PDEs.

Contribution

It introduces a novel formulation of the Tricomi problem incorporating fractional derivatives in a mixed domain setting.

Findings

Existence and uniqueness of solutions established

New methods developed for fractional mixed-type equations

Potential applications in mathematical physics and engineering

Abstract

In this article, the Tricomi problem for a parabolic-hyperbolic type equation in a mixed domain is investigated. Riemann-Liouville fractional derivative participates in the parabolic part of the considerated equation, and the hyperbolic part consists of a degenerate hyperbolic equation of the second kind.