MAXIMUM PRINCIPLES AND APPLICATIONS FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH OPERATORS INVOLVING MITTAG-LEFFLER FUNCTION

In this paper, we formulate and prove two maximum principles to nonlinear fractional differential equations. We consider a fractional derivative operator with Mittag-Leffler function of two parameters in the kernel. These maximum principles are used to establish a pre-norm estimate of solutions, and to derive certain uniqueness and positivity results to related linear and nonlinear fractional initial value problems. MSC 2010: Primary 26A33; Secondary 34K37, 35B50 Key Words and Phrases: fractional order derivative; fractional differential equations; maximum principle; Mittag-Leffler function

Automated summary

This paper formulates and proves two maximum principles for nonlinear fractional differential equations, using a fractional derivative operator with Mittag-Leffler function in the kernel. These principles are applied to establish pre-norm estimates and derive uniqueness and positivity results for linear and nonlinear fractional initial value problems.