Several New Fractional Integral And Sum Inequalities And Their Applications

In recent years,with the development of the theory of fractional calculus equations,the fractional integral inequalities and the fractional sum inequalities are well promoted in the study of the properties of the solutions of fractional differential equations and difference equations.Most of the conclusions can be applied in mathematics,physics,mechanics and optical systems and other fields,so the study of fractional inequalities gradually get the attention of the experts.Based on references[15,16,32,34,35,36],we establish several new fractional integral inequalities and sum inequalities,and obtain some new results.This paper is divided into the following four chapters:Chapter 1 The main problems and the background of this paper are introduced.Chapter 2 Based on the integral inequality in the reference literature[15,16],the following multidimensional integral inequalities are studied:(?)these conclusions are applied to the qualitative research on the solution of fractional calculus equations.Chapter 3 Based on the reference literature[32],Some new discrete fractional order inequalities are studied:(?)the conclusions can be applied to the study of the finalizing properties of the solution of fractional difference equation,such as the uniqueness of solution and the continuous dependence of initial value.Chapter 4 Based on the reference literature[34,35,36],the following discrete fractional order inequalities are given:(?)The definite bounds of unknown functions are obtained,these conclusions are used to study some finalizing properties of the solution of fractional difference equation,such as the boundness of solution and continuous dependence on initial values.