Maximum principle and its application to multi-index Hadamard fractional diffusion equation

Abstract

Abstract This study establishes some new maximum principle which will help to investigate an IBVP for multi-index Hadamard fractional diffusion equation. With the help of the new maximum principle, this paper ensures that the focused multi-index Hadamard fractional diffusion equation possesses at most one classical solution and that the solution depends continuously on its initial boundary value conditions.

Keywords

• Maximum principle
• Hadamard fractional derivative
• Uniformly elliptic operator
• Uniqueness and continuous dependence