A Priori Estimates for Solutions of Boundary Value Problems for Fractional-Order Equations

TL;DR

This paper derives a priori estimates for solutions to boundary value problems of fractional-order diffusion-wave equations using energy inequality methods, providing theoretical bounds for these solutions.

Contribution

It introduces a new approach to obtaining a priori estimates for fractional-order diffusion-wave equations via energy inequalities.

Findings

Established a priori bounds for solutions

Applied energy inequality methods to fractional equations

Provided theoretical insights into boundary value problems

Abstract

We consider boundary value problems of the first and third kind for the diffusionwave equation. By using the method of energy inequalities, we find a priori estimates for the solutions of these boundary value problems.