Positive Solutions Of Boundary Value Problems For Nonlinear Fractional Differential Equations With Integral Boundary Conditions

Nonlinear functional analysis plays a very important role in analysis mathematics and has widespread application to handle nonlinear problems such as physics,engineering,economic mathematics and so on.The further study of nonlinear functional analysis is necessary which has profound theoretical signi?cance and application value.Fractional-order calculus has extended to traditional calculus so it has attracted the great attention of more and more researchers.In this paper, we use the cone theory and the ?xed point theory, to study the existence and uniqueness of positive solutions for nonlinear differential equations with integral boundary conditions.The thesis is divided into three chapters according to contents.Chapter 1, by using the ?xed-point theorem in partially ordered metric spaces,we consider the existence and uniqueness of positive solutions to integral boundary value problems of nonlinear fractional differential equation0+is the standard Riemann-Liouville derivative, f :(0, 1) × [0, +∞) â†' [0, +∞) is continuous. Compared to literature [6][9],the nonlinear f may be singular at t = 0or t = 1. Secondly,compared to literature [10]this article discuss the Mixed monotone operator. Finally,this paper will extend to the higher-order integral equation boundary problem and be more extensively.Chapter 2, by using the ?xed point theorem in cones, we consider the existence and uniqueness of positive solutions to integral boundary value problems of nonlinear fractional differential equation on unbounded domains in Banach space0+is the standard Riemann-Liouville derivative,∫+∞0g(t)tα-1dt < Γ(α).Compared to literature [12] the range of this article is in?nite interval. Secondly,compared to literature [15] this paper using the ?xed point index, come to a positive solution and the existence of multiple positive solutions results for the boundary value problem(2.1.1). Finally, this question is the high-order integral boundary conditions,is more extensive.Chapter 3, by using the Darbo ?xed-point theorem, we consider the existence of positive solutions to integral boundary value problems of nonlinear fractional differential equation on unbounded domains in Banach space0+is the standard Riemann-Liouville derivative,∫+∞0h(t)tα-1dt < Γ(α).In this paper, we use the nature of the non-compactness measure and Darbo ?xed point theorem to get the existence of positive solutions for boundary value problem(3.1.1)on the in?nite interval, And compared to literature [22] the condition σ = 1 to be improved, so that σ advisable to(0, 1]of arbitrary constants.