Boundary value problems for fractional differential equations

In this paper we study the existence of solutions of nonlinear fractional differential equations at resonance. By using the coincidence degree theory, some results on the existence of solutions are obtained.MSC: 34A08, 34B15.

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

[2]  Chuanzhi Bai,et al.  Triple positive solutions for a boundary value problem of nonlinear fractional differential equation , 2008 .

[3]  G. B. Loghmani,et al.  Numerical Methods for Sequential Fractional Differential Equations for Caputo Operator , 2012 .

[4]  J. Mawhin.  Topological degree and boundary value problems for nonlinear differential equations , 1993 .

[5]  E. Montroll,et al.  Anomalous transit-time dispersion in amorphous solids , 1975 .

[6]  R. Magin,et al.  Fractional calculus in viscoelasticity: An experimental study , 2010 .

[7]  Department of Physics,et al.  Some Applications of Fractional Equations , 2003 .

[8]  M. Anwar,et al.  A collocation-shooting method for solving fractional boundary value problems , 2010 .

[9]  Liu Yang,et al.  Nonlocal Boundary Value Problem for Impulsive Differential Equations of Fractional Order , 2011 .

[10]  Ravi P. Agarwal,et al.  Boundary Value Problems for Fractional Differential Equations , 2009 .

[11]  Ahmed Alsaedi,et al.  Existence and Uniqueness of Solutions for Coupled Systems of Higher-Order Nonlinear Fractional Differential Equations , 2010 .

[12]  Bashir Ahmad,et al.  On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order , 2010, Appl. Math. Comput..

[13]  Haibo Chen,et al.  Unique positive solutions for fractional differential equation boundary value problems , 2010, Appl. Math. Lett..

[14]  Weihua Jiang,et al.  The existence of solutions to boundary value problems of fractional differential equations at resona , 2011 .

[15]  Ralf Metzler,et al.  Boundary value problems for fractional diffusion equations , 2000 .

[16]  Yige Zhao,et al.  The existence of multiple positive solutions for boundary value problems of nonlinear fractional differential equations , 2011 .

[17]  D. O’Regan,et al.  Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations , 2010 .

[18]  Nickolai Kosmatov,et al.  A boundary value problem of fractional order at resonance. , 2010 .

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

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

[21]  T F Nonnenmacher,et al.  A fractional calculus approach to self-similar protein dynamics. , 1995, Biophysical journal.

[22]  L. Gaul,et al.  Damping description involving fractional operators , 1991 .

[23]  Hossein Jafari,et al.  Positive solutions of nonlinear fractional boundary value problems using Adomian decomposition method , 2006, Appl. Math. Comput..

[24]  Francesco Mainardi,et al.  Fractional Diffusive Waves , 2001 .

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

[26]  Zhanbing Bai,et al.  Solvability of fractional three-point boundary value problems with nonlinear growth , 2011, Appl. Math. Comput..

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

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

[29]  Wenbin Liu,et al.  Solvability for fractional order boundary value problems at resonance , 2011 .

[30]  R. Metzler,et al.  Relaxation in filled polymers: A fractional calculus approach , 1995 .

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

[32]  Zhanbing Bai,et al.  Solvability for a class of fractional m-point boundary value problem at resonance , 2011, Comput. Math. Appl..

[33]  Zhongli Wei,et al.  Periodic boundary value problems for fractional differential equations involving a Riemann–Liouville fractional derivative☆ , 2010 .

[34]  B. Ahmad,et al.  Impulsive anti-periodic boundary value problem for nonlinear differential equations of fractional or , 2011 .