The Existence of Positive Solution to a Nonlinear Fractional Differential Equation with Integral Boundary Conditions

Advances in Difference Equations

Hanying Feng¹  Meiqiang Feng²  Xiaofang Liu² 

[1] Department of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang, China;School of Applied Science, Beijing Information Science and Technology University, Beijing, China

关键词: Fractional Derivative;    Fixed Point Theorem;    Fractional Differential Equation;    Real Banach Space;    Fixed Point Theory;   

DOI  :  10.1155/2011/546038

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The expression and properties of Green's function for a class of nonlinear fractional differential equations with integral boundary conditions are studied and employed to obtain some results on the existence of positive solutions by using fixed point theorem in cones. The proofs are based on the reduction of the problem considered to the equivalent Fredholm integral equation of the second kind. The results significantly extend and improve many known results even for integer-order cases.

【 授权许可】

CC BY