Time fractional-space fractional power diffusion equation with maximum principle

A maximal principle is developed and demonstrated for the time-fractional diffusion equation. The work also provides an extremum principle for the Caputo fractional derivative, which serves as the foundation for the verifcation of the maximum principle. We use theL۱ approach to solve this problem and approximate Caputo’s fractional derivative, verifying its convergence and stability. Additionally, we have a formula in the space dimension that is equal to the derivative with a fractional power. Furthermore, we give the reformed equation’s maximum principle.

کلیدواژه ها:

Time fractional ، fractional power ، diffusion equation ، maximum principle