IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS IN

This paper is devoted to study the existence of solutions for a class of initial value problems for impulsive fractional differential equations involving the Caputo fractional derivative in a Banach space. The arguments are based upon Mönch’s fixed point theorem and the technique of measures of noncompactness.

[1]  L. Byszewski.  Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem , 1991 .

[2]  S. Szufla,et al.  On the application of measure of noncompactness to existence theorems , 1986 .

[3]  K. Deng,et al.  Exponential Decay of Solutions of Semilinear Parabolic Equations with Nonlocal Initial Conditions , 1993 .

[4]  Sihua Liang,et al.  Positive solutions for boundary value problems of nonlinear fractional differential equation , 2009 .

[5]  Mouffak Benchohra,et al.  Existence results for boundary value problems with non-linear fractional differential equations , 2008 .

[6]  Johnny Henderson,et al.  Existence results for fractional order functional differential equations with infinite delay , 2008 .

[7]  N. Lloyd.  MEASURES OF NONCOMPACTNESS IN BANACH SPACES , 1981 .

[8]  M. Benchohra,et al.  Impulsive differential equations and inclusions , 2006 .

[9]  Shaher Momani,et al.  Some analytical properties of solutions of differential equations of noninteger order , 2004, Int. J. Math. Math. Sci..

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

[11]  D. Baĭnov,et al.  Systems with impulse effect : stability, theory, and applications , 1989 .

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

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

[14]  R. Metzler,et al.  Relaxation in filled polymers: A fractional calculus approach , 1995 .

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

[16]  V. Lakshmikantham,et al.  Theory of Fractional Differential Equations in a Banach Space , 2008 .

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

[18]  Józef Banaś,et al.  On some measures of noncompactness in the space of continuous functions , 2008 .

[19]  H. Mönch,et al.  Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces , 1980 .

[20]  Ravi P. Agarwal,et al.  Fixed Point Theory and Applications , 2001 .

[21]  A. Rodkina,et al.  Measures of noncompactness and condensing operators , 1992 .

[22]  E. W.G.,et al.  On some fractional functional equations , 1995 .

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

[24]  Kou Chun-hai.  Power-type Estimates for a Nonlinear Fractional Differential Equation , 2007 .

[25]  L. Gaul,et al.  Damping description involving fractional operators , 1991 .

[26]  R. Hilfer.  Applications Of Fractional Calculus In Physics , 2000 .

[27]  Mouffak Benchohra,et al.  BOUNDARY VALUE PROBLEMS FOR DIFFERENTIAL EQUATIONS WITH FRACTIONAL ORDER , 2008 .

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

[29]  T F Nonnenmacher,et al.  A fractional calculus approach to self-similar protein dynamics. , 1995, Biophysical journal.

[30]  J. Banaś,et al.  Global asymptotic stability of solutions of a functional integral equation , 2008 .

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

[32]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[33]  H. Mönch,et al.  On the Cauchy problem for ordinary differential equations in Banach spaces , 1982 .

[34]  Song Chao,et al.  Nondecreasing Solutions of a Quadratic Integral Equation of Urysohn Type , 2009 .

[35]  Francesco Mainardi,et al.  Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics , 2012, 1201.0863.

[36]  V. Lakshmikantham,et al.  Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space , 1991 .

[37]  Józef Banas,et al.  An application of a measure of noncompactness in the study of asymptotic stability , 2003, Appl. Math. Lett..

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