Maximum Principle for the Space-Time Fractional Conformable Differential System Involving the Fractional Laplace Operator

Abstract EN

In this paper, the authors consider a IBVP for the time-space fractional PDE with the fractional conformable derivative and the fractional Laplace operator.

A fractional conformable extremum principle is presented and proved.

Based on the extremum principle, a maximum principle for the fractional conformable Laplace system is established.

Furthermore, the maximum principle is applied to the linear space-time fractional Laplace conformable differential system to obtain a new comparison theorem.

Besides that, the uniqueness and continuous dependence of the solution of the above system are also proved.