Oscillation Analysis Of Two Kinds Of Fractional Differential Equations

As part of the qualitative study of fractional differential equations,the theoretical research on the oscillation of fractional differential equations is gradually being developed and perfected,especially for the nonlinear fractional differential equations,the oscillation also need to be studied.Based on previous studies,this paper studies nonlinear fractional differential equation with damping term and a new class of nonlinear neutral fractional differential equation,and gives corresponding oscillation conditions.This article is divided into four chapters.The first chapter,introduction,first introduces the research background of fractional differential equations and the current research situation at home and abroad,secondly introduces the main content of this article,and finally introd-uces some basic concepts used in this article.In chapter two,the oscillation of the following nonlinear fractional differe-ntial equations with damping term is discussed.The methods such as Riccati transformation and H function prove the relevant theorems,and give specific examples to verify the theorems.In chapter three,the oscillation of the following nonlinear fractional differ-ential equations with damping term is discussed.The generalized Riccati transform,the inequality technique and the H function establish two oscillation criteria for determining this equation.In chapter four,we add parameters?based on the existing literature to obtain a new class of nonlinear neutral fractional differential equations.The generalized Riccati transformation and related lemmas are used to prove t-he oscillation of such equations.The main conclusions are verified through spe-cific examples.