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

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 th...

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Bibliographic Details
Published inAdvances in difference equations Vol. 2011; no. 1; pp. 1 - 14
Main Authors Feng, Meiqiang, Liu, Xiaofang, Feng, Hanying
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.01.2011
SpringerOpen
Subjects
Analysis
Difference and Functional Equations
Fractional Models and their Applications
Functional Analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Research Article
Fixed Point Theory
Fixed Point Theorem
Fractional Differential Equation
Fractional Derivative
Real Banach Space
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Summary: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.
ISSN:1687-1839
1687-1847
DOI:10.1155/2011/546038