On the existence and uniqueness of weak solutions to time-fractional elliptic equations with time-dependent variable coefficients

TL;DR

This paper investigates the existence and uniqueness of weak solutions for time-fractional elliptic equations with variable coefficients that depend on time, using advanced mathematical techniques.

Contribution

It introduces a novel combination of the Galerkin method, Lyapunov inequalities, Yoshida approximation, and weak compactness to establish key results.

Findings

Proved existence of weak solutions under certain conditions

Established uniqueness of solutions for the class of equations studied

Developed a new analytical framework for time-fractional elliptic equations

Abstract

This paper is devoted to discussing the existence and uniqueness of weak solutions to time-fractional elliptic equations having time-dependent variable coefficients. To obtain the main result, our strategy is to combine the Galerkin method, a basic inequality for the fractional derivative of convex Lyapunov candidate functions, the Yoshida approximation sequence and the weak compactness argument.