Abstract
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.
Highlights
Many fractional partial differential equations were used for modeling complex dynamic systems of engineering, physics, biology, and many other fields [1,2,3,4]
The maximum principle plays an important role in the study of the complex dynamic systems without certain knowledge of the solutions [5,6,7,8,9,10,11,12,13]
In 2016, Jia and Li [15] applied the maximum principle to the classical solution and weak solution of a time-space fractional diffusion equation
Summary
Many fractional partial differential equations were used for modeling complex dynamic systems of engineering, physics, biology, and many other fields [1,2,3,4]. In 2016, Jia and Li [15] applied the maximum principle to the classical solution and weak solution of a time-space fractional diffusion equation. Motivated by the above works, in this context, the authors investigate the IBVP for a space-time Caputo fractional conformable diffusion system with the fractional Laplace operator. As some applications of the maximum principle, a comparison principle for the space-time fractional Laplace conformable differential system is developed, and the properties of the solution of the system are given, such as the uniqueness and continuous dependence on the initial and boundary condition.
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