Study On Solutions And Properties Of Conformable Fractional Delay Differential Systems

Fractional calculus extends the classic integer-order calculus to any order,which can simulate different complex phenomena.In practical situations,the research process of fractional calculus has a wide range of applications in many fields such as electrochemistry,heat conduction,groundwater flow,porous media,etc.In 2014,R.Khalil and others proposed the concept of conformable fractional derivative.Since it can establish a relationship with classical derivative and satisfies linearity,chain rule,Leibniz's rule,etc.It is of great significance that the study of differential systems in the sense of conformable fractional derivative.The main contents of the paper are as following:First of all,we present the research background and significance of conformable fractional differential systems with delay,the current research status both domestic and overseas,the concepts of classical fractional calculus and conformable fractional integral and derivative,and give relevant lemmas used in the thesis are summarized.Secondly,through the Leray-Schauder nonlinear alternative and the Banach contraction mapping principle,the existence results of the solutions and the sufficient conditions for the unique solution of the nonlinear neutral conformable fractional integro-differential systems are given.Thirdly,the sufficient conditions for the uniqueness and the existence of the solutions are given,regarding the conformable fractional delay differential systems with integral boundary conditions.Finally,the existence,uniqueness and finite-time stability of the solutions of conformable fractional delay differential systems are investigated by using conformable fractional exponential functions and inequalities.