Study On Some Hadamard Fractional Differential Equations On Unbounded Domain

In this thesis,we concentrate on the study of existence and uniqueness of solutions of some Hadamard integro-differential equations on unbounded domains,as well as the monotone iterative sequences and error estimates which converge to the corresponding equations.The thesis is divided into four chapters.In chapter one,we present the research background and the development process of frac-tional calculus theory at beginning.Then,the statements of our main work are put forward.Besides,we introduce the prepax atory knowledge of this thesis.In chapter two,we investigate the existence of the unique solution for a class of Hadamard fractional integral boundary value problem of a Hadamard fractional integro-differential equa-tion.By using monotone iterative technique,we give the monotone iterative sequences for approximating unique solutions and the corresponding error estimation formula.In chapter three,we consider a class of boundary value problem of Hadamard type nonlinear fractional integro-differential equations on unbounded domains.By applying monotone iterative technique and cone theory,we present existence of positive minimal and maximal solutions of Hadamard fractional integro-differential equations.In addition,two computable iterative approximation sequences that uniformly converge to the positive minimal and maximal solutions are given.In chapter four,we investigate a class of Hadamard fractional differential equations with nonlocal multi-point discrete and Hadamard integral boundary conditions.By using monotone iterative method,we not only seek the twin positive solutions of the problem,but also show that the monotone iterative schemes converge to a unique positive solution of the problem and get the error estimate formula.