Nonlinear fractional differential equations with integral boundary value conditions

In this paper, we are interested in the study of the existence of the solutions of a class of nonlinear boundary value problem of fractional differential equations with integral boundary conditions. We make an exhaustive study of the sign of the related Green's function and obtain the exact values for which it is positive on the whole square of definition. The existence of solutions follows from the definition of suitable cones on Banach spaces.

[1]  Sotiris K. Ntouyas,et al.  POSITIVE SOLUTIONS OF ARBITRARY ORDER NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH ADVANCED ARGUMENTS , 2011 .

[2]  Mohamed Abdalla Darwish,et al.  On initial and boundary value problems for fractional order mixed type functional differential inclusions , 2010, Comput. Math. Appl..

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

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

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

[6]  Ahmed Alsaedi,et al.  Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions , 2008 .

[7]  Zheng Zhou,et al.  Existence and global attractivity positive periodic solutions for a discrete model , 2006 .

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

[9]  Juan J. Nieto,et al.  Second-Order Boundary Value Problem with Integral Boundary Conditions , 2011 .

[10]  A. Cabada,et al.  Positive solutions of nonlinear fractional differential equations with integral boundary value conditions , 2012 .

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

[12]  Z. Tomovski,et al.  Generalized Cauchy type problems for nonlinear fractional differential equations with composite fractional derivative operator , 2012 .

[13]  Yonghong Wu,et al.  Second-order nonlinear singular Sturm-Liouville problems with integral boundary conditions , 2009, Appl. Math. Comput..

[14]  Ewa Girejko,et al.  A sufficient condition of viability for fractional differential equations with the Caputo derivative , 2011 .

[15]  Alberto Cabada,et al.  An Existence Result for Nonlinear Fractional Differential Equations on Banach Spaces , 2009 .

[16]  Weigao Ge,et al.  New Existence Results for Higher-Order Nonlinear Fractional Differential Equation with Integral Boundary Conditions , 2010 .

[17]  Ahmed Alsaedi,et al.  A study of nonlinear Langevin equation involving two fractional orders in different intervals , 2012 .

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

[19]  Haiyan Wang,et al.  On the number of positive solutions of nonlinear systems , 2003 .

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

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

[22]  Weigao Ge,et al.  Existence result of second-order differential equations with integral boundary conditions at resonance , 2009 .

[23]  Ravi P. Agarwal,et al.  On nonlocal fractional boundary value problems , 2011 .

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

[25]  Rathinasamy Sakthivel,et al.  Existence of solutions for nonlinear fractional stochastic differential equations , 2013 .

[26]  Hussein A. H. Salem,et al.  Fractional order boundary value problem with integral boundary conditions involving Pettis integral , 2011 .

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

[28]  Mouffak Benchohra,et al.  Boundary value problems for differential inclusions with fractional order , 2008 .

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

[30]  Chuanzhi Bai,et al.  Impulsive periodic boundary value problems for fractional differential equation involving Riemann–Liouville sequential fractional derivative , 2011 .

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

[32]  W. Ames,et al.  Nonlinear problems in abstract cones , 1988 .

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

[34]  Rudolf Gorenflo,et al.  Nonlinear two-term time fractional diffusion-wave problem , 2010 .

[35]  Nasser-eddine Tatar,et al.  Existence and uniqueness for a problem involving Hilfer fractional derivative , 2012, Comput. Math. Appl..

[36]  Ravi P. Agarwal,et al.  EXISTENCE OF SOLUTIONS FOR IMPULSIVE ANTI-PERIODIC BOUNDARY VALUE PROBLEMS OF FRACTIONAL SEMILINEAR EVOLUTION EQUATIONS , 2011 .