Some existence results for impulsive nonlinear fractional differential equations with mixed boundary conditions

This paper investigates the existence and uniqueness of solutions for an impulsive mixed boundary value problem of nonlinear differential equations of fractional order @[email protected]?(1,2]. Our results are based on some standard fixed point theorems. Some examples are presented to illustrate the main results.

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

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

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

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

[5]  Yong Zhou,et al.  A class of fractional evolution equations and optimal controls , 2011 .

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

[7]  S. T. Zavalishchin,et al.  Dynamic Impulse Systems: Theory and Applications , 1997 .

[8]  Zhanbing Bai,et al.  Existence results for the three-point impulsive boundary value problem involving fractional differential equations , 2010, Comput. Math. Appl..

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

[10]  Yong Zhou,et al.  EXISTENCE AND UNIQUENESS FOR FRACTIONAL NEUTRAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY , 2009 .

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

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

[13]  Ravi P. Agarwal,et al.  Existence of fractional neutral functional differential equations , 2010, Comput. Math. Appl..

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

[15]  E. Zeidler Nonlinear functional analysis and its applications , 1988 .

[16]  A. Samoilenko,et al.  Impulsive differential equations , 1995 .

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

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

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

[20]  Juan J. Nieto,et al.  Existence results for a nondensely-defined impulsive neutral differential equation with state-dependent delay , 2010 .

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

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

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

[24]  Ivan Avramidi,et al.  Heat Kernel Asymptotics of Zaremba Boundary Value Problem , 2001 .

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

[26]  Bashir Ahmad,et al.  Existence of solutions for fractional differential equations of order q∈(2,3] with anti-periodic boundary conditions , 2010 .

[27]  M. van den Berg,et al.  Heat Content Asymptotics for Riemannian Manifolds with Zaremba Boundary Conditions , 2005, math-ph/0506076.

[28]  Sotiris K. Ntouyas,et al.  Positive solutions of the three-point boundary value problem for fractional-order differential equations with an advanced argument , 2011 .

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

[30]  S. Sivasundaram,et al.  Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations , 2009 .

[31]  Lihong Zhang,et al.  Extremal solutions for the first order impulsive functional differential equations with upper and lower solutions in reversed order , 2010, J. Comput. Appl. Math..

[32]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

[33]  Xiyue Huang,et al.  The existence and uniqueness of mild solutions for impulsive fractional equations with nonlocal conditions and infinite delay , 2010 .