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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.

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