Existence Results and the Monotone Iterative Technique for Nonlinear Fractional Differential Systems with Coupled Four-Point Boundary Value Problems

By establishing a comparison result and using the monotone iterative technique combined with the method of upper and lower solutions, we investigate the existence of solutions for nonlinear fractional differential systems with coupled four-point boundary value problems.

[1]  Josimar Ramirez,et al.  Generalized Monotone Iterative Technique for Caputo Fractional Differential Equation with Periodic Boundary Condition via Initial Value Problem , 2012 .

[2]  Lin Zhigui,et al.  The blow-up rate for a system of heat equations with nonlinear boundary conditions , 1998 .

[3]  Ailing Shi,et al.  Upper and lower solutions method and a fractional differential equation boundary value problem. , 2009 .

[4]  W. Marsden.  I and J , 2012 .

[5]  Lishan Liu,et al.  The Existence of Solutions for Four-Point Coupled Boundary Value Problems of Fractional Differential Equations at Resonance , 2014 .

[6]  Xingqiu Zhang,et al.  Uniqueness and Existence of Positive Solutions for Singular Differential Systems with Coupled Integral Boundary Value Problems , 2013 .

[7]  Zhigui Lin,et al.  Blow-up analysis for a system of heat equations coupled through a nonlinear boundary condition , 2001, Appl. Math. Lett..

[8]  H. Amann.  Parabolic evolution equations and nonlinear boundary conditions , 1988 .

[9]  Yumei Zou,et al.  Monotone iterative method for differential systems with coupled integral boundary value problems , 2013 .

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

[11]  A. Vatsala,et al.  Monotone iterative technique for fractional differential equations with periodic boundary conditions , 2009 .

[12]  Guotao Wang,et al.  Monotone iterative technique for boundary value problems of a nonlinear fractional differential equation with deviating arguments , 2012, J. Comput. Appl. Math..

[13]  M. Al-Refai,et al.  Monotone iterative sequences for nonlinear boundary value problems of fractional order , 2011 .

[14]  Legang Lin,et al.  Method of upper and lower solutions for fractional differential equations , 2012 .

[15]  Zhongli Wei,et al.  Initial value problems for fractional differential equations involving Riemann–Liouville sequential fractional derivative , 2010 .

[16]  Shuqin Zhang,et al.  Monotone iterative method for initial value problem involving Riemann–Liouville fractional derivatives , 2009 .

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

[18]  Rahmat Ali Khan,et al.  Positive solutions to singular system with four-point coupled boundary conditions , 2012 .

[19]  Keng Deng,et al.  Blow-up rates for parabolic systems , 1996 .

[20]  D. O’Regan,et al.  Multiple positive solutions to systems of nonlinear semipositone fractional differential equations with coupled boundary conditions , 2012 .

[21]  Jingxian Sun,et al.  On existence of positive solutions of coupled integral boundary value problems for a nonlinear singular superlinear differential system , 2012 .

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

[23]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies) , 2006 .

[24]  Shuqin Zhang,et al.  The existence of a solution for a fractional differential equation with nonlinear boundary conditions considered using upper and lower solutions in reverse order , 2011, Comput. Math. Appl..

[25]  Tadeusz Jankowski,et al.  Boundary problems for fractional differential equations , 2014, Appl. Math. Lett..

[26]  H. Kober.  ON FRACTIONAL INTEGRALS AND DERIVATIVES , 1940 .

[27]  Keng Deng,et al.  Global existence and blow-up for a system of heat equations with non-linear boundary conditions* , 1995 .