An Existence Result for Nonlinear Fractional Differential Equations on Banach Spaces

The aim of this paper is to investigate a class of boundary value problem for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of noncompactness.

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

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

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

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

[5]  A. Lesfari Surveys in Mathematics and its Applications , 2010 .

[6]  S. Pečiulytė,et al.  Sturm‐Liouville problem for stationary differential operator with nonlocal integral boundary condition , 2010 .

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

[8]  G. Adomian,et al.  Cellular systems and aging models , 1985 .

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

[10]  A. Arara,et al.  FUZZY SOLUTIONS FOR BOUNDARY VALUE PROBLEMS WITH INTEGRAL BOUNDARY CONDITIONS , 2006 .

[11]  I. Podlubny,et al.  Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives , 2005, math-ph/0512028.

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

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

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

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

[16]  Gennaro Infante,et al.  Eigenvalues and positive solutions of odes involving integral boundary conditions , 2005 .

[17]  A. Sändig,et al.  Nonlinear Differential Equations , 1980 .

[18]  S. Pečiulytė,et al.  Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions , 2006 .

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

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

[21]  S. Gong The Bieberbach Conjecture , 1999 .

[22]  E. C. Oliveira,et al.  Differentiation to fractional orders and the fractional telegraph equation , 2008 .

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

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

[25]  Saudi Arabia Ahmad, B., Nieto, J.J. Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions , 2009 .

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

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

[28]  V. Lakshmikantham,et al.  Nonlinear differential equations in abstract spaces , 1981 .

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

[30]  M. Benchohra,et al.  Functional Differential Inclusions with Integral Boundary Conditions , 2007 .

[31]  Sachin Bhalekar,et al.  Boundary value problems for multi-term fractional differential equations , 2008 .

[32]  M. Benchohra,et al.  Uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces , 2006 .

[33]  Igor Podlubny,et al.  Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation , 2001, math/0110241.

[34]  Bashir Ahmad,et al.  Existence of Solutions for Fractional Differential Inclusions with Antiperiodic Boundary Conditions , 2009 .

[35]  Juan J. Nieto,et al.  The Method of Upper and Lower Solutions for Second Order Differential Inclusions with Integral Boundary Conditions , 2010 .

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

[37]  Bashir Ahmad,et al.  Existence Results for Nonlinear Boundary Value Problems of Fractional Integrodifferential Equations with Integral Boundary Conditions , 2009 .