Existence Of Solutions For Three Classes Boundary Value Problems Of Fractional Impulsive Hahn Difference Equation

In recent years,the development of quantum calculus has been very rapid,playing an important role in the fields of dynamic systems,spectral analysis,quantum models and so on.Due to its wide application,fractional calculus and fractional differential equations have attracted the attention of many experts and scholars,A lot of new re-search results have emerged.Impulsive differential equations are an important branch of differential equations.They have important applications in modeling and can ac-curately reflect the changing laws of things.Therefore,they have high research value,fractional order q-Calculus is a generalization of fractional calculus,often used as a mathematical modeling tool for practical problems.Based on them,Hahn calculus came into being.In view of the extensive application of the former in real life,the development of fractional order Hahn difference Research on equation-related prob-lems has important theoretical significance and practical value.At present,there are few research results on boundary value problems of fractional-order impulsive Hahn difference equations.This paper explores the existence of solutions to three types of ordered fractional impulsive Hahn difference equations based on the existing literature:The first category,the existence of impulsive solutions of the fractional Hahn difference equations defined on the infinite interval.First,in order to prove the com-pactness of the operator,a modified compactness criterion is introduced.Second,it is used under the assumption that some conditions are true.Leggett-Williams fixed point theorem obtains the existence of the solution of the boundary value problem.The monotone iterative technique is used to obtain the boundary value problem.There are two positive solutions.On this basis,the Banach compression mapping principle is used to obtain the unique solution of the boundary value problem.Finally,give relevant examples to illustrate.The second type,the existence of solutions for fractional impulsive Hahn difference equations with anti-periodic boundary value conditions,when this boundary value problem satisfies certain specific conditions,the solution of the boundary value problem is first known by Leray-Schauder nonlinear decision theorem Existence,and then,using Boyd and Wong fixed point theorem,Rothe fixed point theory to get a unique solution to this boundary value problem.Finally,give relevant examples.The third type,the existence of solutions to the boundary value problem of frac-tional Hahn difference equations with perturbation terms,in order to obtain the formal solution of the equation,first define the exponential function and give its related prop-erties,and then use the Banach compression mapping principle and related index It is reasonable to find that the boundary value problem has a unique solution and give relevant examples to illustrate the validity of the results.