| The study of boundary value problem on half-infinite interval has certain practical andtheoretical significance. The study of integer order boundary value problem onhalf-infinite interval has made a series of achievements. Using the Krein-Rutmanfixed-point theorem and fixed-point index theory, this paper studies the existence of atleast one positive solution for second order two-point boundary value problem onhalf-infinite interval by solving the Green’s function of the equation, establishing asuitable space, giving the appropriate norm and defining a regeneration cone, where thenonlinear term contains first order derivative, and may be singular at any point.The boundary value problem of fractional differential equation is a new subject, whichis applied in physics, chemistry, medicine, meteorology and many other fields, such asmedical image processing, seismic singularity analysis, etc. Firstly, this paper introducesthe basic definition and basic property of fractional differential equation, gives the Green’sfunction of fractional multi-point boundary value problem on half-infinite interval andstudies its properties, then discusses the existence of solutions of the boundary valueproblem by using the contraction mapping principle. |
