POSITIVE SOLUTIONS OF ARBITRARY ORDER NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH ADVANCED ARGUMENTS

In this paper, we investigate the existence and uniqueness of positive solutions to arbitrary order nonlinear fractional differential equations with advanced arguments. By applying some known fixed point theorems, sufficient conditions for the existence and uniqueness of positive solutions are established.

[1]  J. Trujillo,et al.  The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces , 2010, Nonlinear Analysis: Theory, Methods & Applications.

[2]  Tadeusz Jankowski,et al.  Positive solutions for fourth-order differential equations with deviating arguments and integral boundary conditions , 2010 .

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

[4]  Shuqin Zhang,et al.  Positive solutions to singular boundary value problem for nonlinear fractional differential equation , 2010, Comput. Math. Appl..

[5]  Guotao Wang,et al.  Integral boundary value problems for first order integro-differential equations with deviating arguments , 2009 .

[6]  Juan J. Nieto,et al.  Some new existence results for fractional differential inclusions with boundary conditions , 2009, Math. Comput. Model..

[7]  Aleksandar M. Spasic,et al.  Finite-time stability analysis of fractional order time-delay systems: Gronwall's approach , 2009, Math. Comput. Model..

[8]  V. Lakshmikantham,et al.  Nonlinear Integral Equations in Abstract Spaces , 1996 .

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

[10]  Christopher S. Goodrich,et al.  Existence of a positive solution to a class of fractional differential equations , 2010, Applied Mathematics Letters.

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

[12]  K. Balachandran,et al.  On local attractivity of solutions of a functional integral equation of fractional order with deviating arguments , 2010 .

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

[14]  D. O’Regan,et al.  Positive Solutions of Differential, Difference and Integral Equations , 1998 .

[15]  Juan J. Nieto,et al.  Maximum principles for fractional differential equations derived from Mittag-Leffler functions , 2010, Appl. Math. Lett..

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

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

[18]  Jurang Yan,et al.  Oscillation of first-order impulsive differential equations with advanced argument , 2001 .

[19]  J. Nieto,et al.  Existence of Periodic Solution for a Nonlinear Fractional Differential Equation , 2009 .

[20]  On some nonlinear ordinary differential equations with advanced arguments , 2003 .

[21]  Tadeusz Jankowski.  First-order advanced difference equations , 2010, Appl. Math. Comput..

[22]  S. Sivasundaram,et al.  Existence of solutions for impulsive integral boundary value problems of fractional order , 2010 .

[23]  Guotao Wang,et al.  Boundary value problems for systems of nonlinear integro-differential equations with deviating arguments , 2010, J. Comput. Appl. Math..

[24]  Chen Yang,et al.  Positive solutions of the three-point boundary value problem for second order differential equations with an advanced argument , 2006 .

[25]  S. Ntouyas,et al.  Monotonic solutions of a perturbed quadratic fractional integral equation , 2009 .

[26]  H. Srivastava,et al.  THEORY AND APPLICATIONS OF FRACTIONAL DIFFERENTIAL EQUATIONS. NORTH-HOLLAND MATHEMATICS STUDIES , 2006 .

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

[28]  O. Agrawal,et al.  Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering , 2007 .

[29]  Gisèle M. Mophou,et al.  Existence and uniqueness of mild solutions to impulsive fractional differential equations , 2010 .

[30]  Ravi P. Agarwal,et al.  An existence result for a superlinear fractional differential equation , 2010, Appl. Math. Lett..