Positive solutions for fractional four-point boundary value problems☆

Abstract In this paper, a fractional four-point boundary value problem is considered. By means of fixed-point theorems and successive iteration method, some results on the existence, multiplicity and uniqueness of positive solutions are obtained.

[1]  Weigao Ge,et al.  Multiple positive solutions for second-order four-point boundary value problem , 2007, Comput. Math. Appl..

[2]  Abdelghani Ouahab,et al.  Some results for fractional boundary value problem of differential inclusions , 2008 .

[3]  F. Mainardi,et al.  Fractals and fractional calculus in continuum mechanics , 1997 .

[4]  W. Ge,et al.  Positive solutions for a four-point boundary value problem with the p-Laplacian , 2008 .

[5]  Shuqin Zhang,et al.  EXISTENCE OF SOLUTION FOR A BOUNDARY VALUE PROBLEM OF FRACTIONAL ORDER * * Supported by the National 973-Project from MOST and Trans-Century Training Programme Foundation for the Talents by Ministry of Education and the Postdoctoral Foundation of China. , 2006 .

[6]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[7]  Om P. Agrawal,et al.  Formulation of Euler–Lagrange equations for fractional variational problems , 2002 .

[8]  R. Bagley,et al.  On the Fractional Calculus Model of Viscoelastic Behavior , 1986 .

[9]  Sihua Liang,et al.  Positive solutions for boundary value problems of nonlinear fractional differential equation , 2009 .

[10]  R. Leggett,et al.  Multiple positive fixed points of nonlinear operators on ordered Banach spaces , 1979 .

[11]  M. Benchohra,et al.  Boundary value problems for differential equations with fractional order and nonlocal conditions , 2009 .

[12]  Meng Zhang,et al.  Positive solutions for boundary value problems of nonlinear fractional differential equations , 2011, Appl. Math. Comput..

[13]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[14]  Zaid M. Odibat,et al.  Computing eigenelements of boundary value problems with fractional derivatives , 2009, Appl. Math. Comput..

[15]  I. Podlubny.  Fractional differential equations , 1998 .

[16]  Hui Fang,et al.  Multiple periodic solutions for a discrete time model of plankton allelopathy , 2006 .

[17]  Hussein A. H. Salem,et al.  On the fractional order m-point boundary value problem in reflexive Banach spaces and weak topologies , 2009 .

[18]  Francesco Mainardi,et al.  Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics , 2012, 1201.0863.

[19]  Zhanbing Bai,et al.  Positive solutions for boundary value problem of nonlinear fractional differential equation , 2005 .

[20]  W. Ge,et al.  Existence of multiple positive solutions for Sturm–Liouville-like four-point boundary value problem with p-Laplacian☆ , 2008 .

[21]  Xinwei Su,et al.  Boundary value problem for a coupled system of nonlinear fractional differential equations , 2009, Appl. Math. Lett..