Existence and uniqueness of solutions for a nonlinear fractional differential equation

In this paper we prove the existence and uniqueness of solutions for a class of the nonlinear fractional differential equation with initial condition and investigate the dependence of the solution on the order of the differential equation and on the initial condition. Then we give an example to demonstrate the main results.

[1]  N. Ford,et al.  Analysis of Fractional Differential Equations , 2002 .

[2]  Dumitru Baleanu,et al.  On the global existence of solutions to a class of fractional differential equations , 2010, Comput. Math. Appl..

[3]  C. F. Li,et al.  Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations , 2010, Comput. Math. Appl..

[4]  V. Lakshmikantham,et al.  Theory of fractional functional differential equations , 2008 .

[5]  Yong Zhou,et al.  Positive solutions for multipoint boundary value problem of fractional differential equations , 2012 .

[6]  Wei Wei,et al.  EXISTENCE AND UNIQUENESS RESULTS FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH BOUNDARY VALUE CONDITIONS , 2011 .

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

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

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

[10]  Gaston M. N’Guérékata,et al.  A Cauchy problem for some fractional abstract differential equation with non local conditions , 2009 .

[11]  An inverse coefficient problem with nonlinear parabolic equation , 2010 .

[12]  M. Caputo.  Linear Models of Dissipation whose Q is almost Frequency Independent-II , 1967 .

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

[14]  Gaston M. N'Guérékata,et al.  Optimal control of a fractional diffusion equation with state constraints , 2011, Comput. Math. Appl..

[15]  Shuqin Zhang,et al.  The Existence of a Positive Solution for a Nonlinear Fractional Differential Equation , 2000 .

[16]  Luigi Rodino,et al.  Existence and Uniqueness for a Nonlinear Fractional Differential Equation , 1996 .

[17]  Guoqing Chai,et al.  Existence results for boundary value problems of nonlinear fractional differential equations , 2011, Comput. Math. Appl..

[18]  Bashir Ahmad,et al.  Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions , 2009, Comput. Math. Appl..