Tricomi type boundary value problem with integral conjugation condition for a mixed type equation with Hilfer fractional operator

TL;DR

This paper investigates a Tricomi boundary value problem involving a Hilfer fractional differential operator, establishing unique solvability using integral equations and energy methods for a mixed type equation.

Contribution

It introduces a novel boundary problem with integral conjugation for a mixed type equation involving Hilfer fractional derivatives and proves its unique solvability.

Findings

Unique solvability of the problem established

Method of integral equations applied successfully

Energy integral method used for proof

Abstract

In this work, The Tricomi type boundary problem with integral conjugation condition on the type-changing line for the mixed type equation with Hilfer fractional differential operator has been considered. Using method of integral equations, energy integral's method, a unique solvability of the formulated problem has been proved.