Solvability for a class of fractional m-point boundary value problem at resonance

In this paper, the following fractional ordinary differential equation boundary value problem: D"0"+^@au(t)=f(t,u(t),D"0"+^@a^-^1u(t))+e(t),0R is continuous and e@?L^1[0,1], and @b"i@?R,i=1,2,...,m-2,0<@h"1<@h"2<...<@h"m"-"2<1 are given constants such that @?"i"="1^m^-^2@b"i@h"i^@a^-^1=1. By using the coincidence degree theory, some existence results of solutions can be established.

[1]  V. Lakshmikantham,et al.  Theory of Fractional Dynamic Systems , 2009 .

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

[3]  Bashir Ahmad,et al.  Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential Equations , 2009 .

[4]  Bing Liu,et al.  Solvability of multi-point boundary value problem at resonance (III) , 2003, Appl. Math. Comput..

[5]  Ravi P. Agarwal,et al.  A Survey on Semilinear Differential Equations and Inclusions Involving Riemann-Liouville Fractional Derivative , 2009 .

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

[7]  J. Mawhin Topological degree methods in nonlinear boundary value problems , 1979 .

[8]  Hu Wei-min,et al.  Positive Solution for Boundary Value Problem of Nonlinear Fractional Differential Equation , 2011 .

[9]  V. Anh,et al.  FRACTIONAL DIFFERENTIAL EQUATIONS DRIVEN BY L , 2003 .

[10]  V. Lakshmikantham,et al.  A Krasnoselskii–Krein-type uniqueness result for fractional differential equations , 2009 .

[11]  Zhanbing Bai,et al.  On positive solutions of a nonlocal fractional boundary value problem , 2010 .

[12]  R. Agarwal,et al.  A Survey on Existence Results for Boundary Value Problems of Nonlinear Fractional Differential Equations and Inclusions , 2010 .

[13]  C. P. Gupta A second order m -point boundary value problem at resonance , 1995 .

[14]  Yong Zhou,et al.  Existence and uniqueness of fractional functional differential equations with unbounded delay , 2008 .

[15]  Yong Zhou,et al.  Existence and uniqueness for p-type fractional neutral differential equations☆ , 2009 .

[16]  Tingting Qiu,et al.  Positive solutions for boundary value problem of nonlinear fractional differential equation. , 2008 .

[17]  Johnny Henderson,et al.  Fractional functional differential inclusions with finite delay , 2009 .

[18]  V. Lakshmikantham,et al.  Basic theory of fractional differential equations , 2008 .

[19]  Yong Zhou,et al.  Nonlocal Cauchy problem for fractional evolution equations , 2010 .

[20]  Yong Zhou,et al.  EXISTENCE AND UNIQUENESS FOR FRACTIONAL NEUTRAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY , 2009 .

[21]  Zhanbing Bai On solutions of some fractional $m$-point boundary value problems at resonance , 2010 .

[22]  Varsha Daftardar-Gejji,et al.  Existence of positive solutions of nonlinear fractional differential equations , 2003 .

[23]  Zhanbing Bai,et al.  Existence of solutions for nonlinear fractional three-point boundary value problems at resonance , 2011 .

[24]  Ahmed M. A. El-Sayed,et al.  Nonlinear functional differential equations of arbitrary orders , 1998 .

[25]  Bing Liu,et al.  Solvability of multi-point boundary value problem at resonance (II) , 2003, Appl. Math. Comput..

[26]  K. Diethelm The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type , 2010 .

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

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

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

[30]  J. Webb,et al.  Solvability ofm-Point Boundary Value Problems with Nonlinear Growth , 1997 .