Comparison Principle and Solution Bound of Fractional Differential Equations

Abstract

The comparison principle of fractional differential equations is discussed in this paper. We obtain two kinds of comparison principle which are related to the functions in the right hand side of equations, and the order of fractional derivative, respectively. By using the comparison principle, the boundedness of fractional Lorenz system and fractional Lorenz-like system are studied numerically. Numerical simulations are carried out which demonstrate our theoretical analysis.