Multi-order fractional nonlinear evolution equations system

Abstract

In this paper, the existence and uniqueness of a solution to a multi-order fractional nonlinear evolution equations system are studied by applying Banach’s Fixed Point Theorem and some properties of solution operators associated with the system. The results show that the solution to the system exists uniquely under some Lipschitz conditions on the nonlinear part of the system. The regularity of the system is also discussed here. The applications of our results to some systems such as non-local reaction–subdiffusion system, chemotaxis–subdiffusion system, and non-local reaction–subdiffusion system with chemotaxis are given.

Keywords

• Multi-order fractional nonlinear evolution equations system
• Mild solution
• Classical solution
• Strict solution