Well-posedness of time-fractional, advection-diffusion-reaction equations

TL;DR

This paper proves the well-posedness of a broad class of time-fractional advection-diffusion-reaction equations with variable coefficients and low-regularity initial data using innovative energy methods and fractional inequalities.

Contribution

It introduces new energy techniques and fractional Gronwall inequalities to establish well-posedness for complex fractional PDEs with variable coefficients.

Findings

Established well-posedness for general time-fractional PDEs

Developed novel energy methods for fractional equations

Applied fractional Gronwall inequality to analyze solutions

Abstract

We establish the well-posedness of an initial-boundary value problem for a general class of time-fractional, advection-diffusion-reaction equations, allowing space- and time-dependent coefficients as well as initial data that may have low regularity. Our analysis relies on novel energy methods in combination with a fractional Gronwall inequality and properties of fractional integrals.