Existence Of Solutions For Boundary Value Problems With Three Classes Systems Of Fractional Q-differences

Thomas introduced the concept of q-integral in 1869.Jackson defined a more gen-eralized q-integral in 1910.Since then the concept of q-calculus also will be generated.The q-difference theory is an important part of the discrete mathematics.It has been studied and discussed by more and more scholars.Our main work focuses on three aspects,one is the existence of solutions for the sequential Caputo-type fractional order q-differences system.the second is the existence and uniqueness of solutions for Caputo-type fractional order q-differential systems with functional boundary value problems.And the third is the existence and uniqueness of solutions for Riemann-Liouville type fractional order q-difference system with multi-point boundary conditions.The paper consists of five parts.The main contents are as follows:Chapter one is the introduction part.First of all,we sketch the historical back-ground?relevance of significance and research status for the q-difference equation,followed by an overview of the main contents of this paper.The second chapter is the preliminary part.It mainly introduces some relevant definitions,properties and lemmas used in the dissertation.The third chapter studies the existence of solutions for the sequential Caputo-type fractional order q-differences system.Firstly,using q-exponential,a representation for the solution to this equation is given.Then the existence theorem of solutions are proven by using Leray-Schauder alternative theorem,Krasnoselskii fixed point theorem.The fourth chapter studies the existence and uniqueness of solutions for Caputo-type fractional order q-differential systems with functional boundary value problems.According to the expression of the system solution,four operators axe constructed and a new operator is defined on the basis of it.Then we prove that the existence of the solution of the system transforms to prove whether the new operator has fixed point,and then uses Krasnoselskii fixed point theorem and Perov's fixed point theorem prove the existence and uniqueness of the solution on the basis of the assumptions.The fifth chapter mainly studies the existence and uniqueness of solutions for Riemann-Liouville type fractional order q-difference systems with multi-point bound-ary conditions.Under the relevant assumptions,the existence and uniqueness of the system solution are proved by Schauder fixed point theorem and Banach contraction mapping principle.