DOI: 10.13763/j.cnki.jhebnu.nse.2018.03.003

Existence of Solutions for a Class of Boundary Value Problems of Fractional Differential Equations
FENG Lijie
School of Mathematics, Tianjin University, Tianjin 300350, China
Abstract:
A class of boundary value problems of fractional differential equations are investigated,which involves the Riemman-Liouville fractional derivative of the unknown function in the nonlinear term.Existence of two solutions is obtained by applying the properties of Green function and the monotone iteration technique.Two iterative sequences are established to approximate the solutions.An example is given to illustrate the validity of the result.

KILBAS A A,SRIVASTAVA H M,TRUJILLO J J.Theory and Applications of Fractional Differential Equations[M].London/New York:Elsevier,2006.
白占兵.分数阶微分方程边值问题理论及应用[M].北京:中国科学技术出版社,2012.
BAI Z B,LU H S.Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation[J].Journal of Mathematical Analysis and Applications,2005,311(2):495-505.doi:10.1016/j.jmaa.2005.02.052.
EI-SHAHED M,SHAMMAKH W M.Existence of Positive Solutions for m-point Boundary Value Problem for Nonlinear Fractional Differential Equation[J].Abstract and Applied Analysis,2011(3):1-15.doi:10.1155/2011/986575.
SUN Y P,ZHAO M.Positive Solutions for a Class of Fractional Differential Equations with Integral Boundary Conditions[J].Applied Mathematics Letters,2014,34(1):17-21.doi:10.1016/j.aml.2014.03.008.
GAO H L,HAN X L.Existence of Positive Solutions for Fractional Differential Equation with Nonlocal Boundary Condition[J].International Journal of Differential Equations,2011,328394:1-10.doi:10.1155/2011/328394.
ZHANG X Q.Positive Solutions for a Class of Singular Fractional Differential Equation with Infinite-point Boundary Value Conditions[J].Applied Mathematics Letters,2015,39:22-27.doi:10.1016/j.aml.2014.08.008.
GUO L M,LIU L S,WU Y H.Existence of Positive Solutions for Singular Fractional Differential Equations with Infinite-point Boundary Conditions[J].Nonlinear Analysis-modelling and Control,2016,21(5):635-650.doi:10.15388/NA.2016.05.005.
ZHAI C B,WANG L.Some Existence,Uniqueness Results on Positive Solutions for a Fractional Differential Equation with Infinite-point Boundary Conditions[J].Nonlinear Analysis Modelling and Control,2017,22(4):566-577.doi:10.15388/NA.2017.04.010.
AMANN H.Fixed Point Equations and Nonlinear Eigenvalue Problems in Order Banach Spaces[J].SIAM Rev,1976,18(4):620-709. doi:10.1137/1018114.