Existence of S-asymptotically ω-periodic solutions for fractional order functional integro-differential equations with infinite delay

Abstract We study S -asymptotically ω -periodic solutions of the abstract fractional equation u ′ = ∂ − α + 1 A u + f ( t , u t ) , 1 α 2 , where A is a linear operator of sectorial type μ 0 .

[1]  Eduardo Cuesta,et al.  A Numerical Method for an Integro-Differential Equation with Memory in Banach Spaces: Qualitative Properties , 2003, SIAM J. Numer. Anal..

[2]  Abdelghani Ouahab,et al.  Some results for fractional boundary value problem of differential inclusions , 2008 .

[3]  Wang Ke,et al.  Massera-Type theorem and asymptotically periodic Logistic equations☆ , 2006 .

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

[5]  Emilia Bazhlekova,et al.  Fractional evolution equations in Banach spaces , 2001 .

[6]  Carlos Lizama,et al.  Almost automorphic solutions to a class of semilinear fractional differential equations , 2008, Appl. Math. Lett..

[7]  S. Hanson,et al.  Real World Applications , 1997 .

[8]  Carlos Lizama,et al.  Rates of approximation and ergodic limits of regularized operator families , 2003, J. Approx. Theory.

[9]  Carlos Lizama,et al.  Regularized Solutions for Abstract Volterra Equations , 2000 .

[10]  Hernán R. Henríquez,et al.  On S-asymptotically ω-periodic functions on Banach spaces and applications , 2008 .

[11]  Anatoly N. Kochubei,et al.  Cauchy problem for fractional diffusion equations , 2003 .

[12]  Carlos Lizama,et al.  ON PERTURBATION OF K-REGULARIZED RESOLVENT FAMILIES , 2003 .

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

[14]  V. Lakshmikantham,et al.  THEORY OF FRACTIONAL DIFFERENTIAL INEQUALITIES AND APPLICATIONS , 2007 .

[15]  V. Anh,et al.  Fractional Differential Equations Driven by Levy Noise , 2003 .

[16]  Claudio Cuevas,et al.  S-asymptotically omega-periodic solutions of semilinear fractional integro-differential equations , 2009, Appl. Math. Lett..

[17]  A. G. Ibrahim,et al.  Multivalued fractional differential equations , 1995 .

[18]  Michelle Pierri,et al.  A note on S-asymptotically periodic functions , 2009 .

[19]  Carlos Lizama,et al.  On approximation and representation of K-regularized resolvent families , 2001 .

[20]  Claudio Cuevas,et al.  Existence and uniqueness of pseudo almost periodic solutions of semilinear Cauchy problems with non dense domain , 2001 .

[21]  Johnny Henderson,et al.  Existence Results for Fractional Functional Differential Inclusions with Infinite Delay and Applications to Control Theory , 2008 .

[22]  Eduardo Cuesta,et al.  ASYMPTOTIC BEHAVIOUR OF THE SOLUTIONS OF FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS AND SOME TIME DISCRETIZATIONS , 2007 .

[23]  Jeng-Chung Chen,et al.  ASYMPTOTIC BEHAVIOR OF (a, k)-REGULARIZED RESOLVENT FAMILIES AT ZERO , 2006 .

[24]  G. Prato,et al.  Existence and regularity results for an integral equation with infinite delay in a Banach space , 1988 .

[25]  C. Lizama,et al.  Almost automorphic solutions to integral equations on the line , 2009 .

[26]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[27]  H. Henríquez,et al.  EXISTENCE OF S-ASYMPTOTICALLY ω-PERIODIC SOLUTIONS FOR ABSTRACT NEUTRAL EQUATIONS , 2008, Bulletin of the Australian Mathematical Society.

[28]  Johnny Henderson,et al.  Fractional functional differential inclusions with finite delay , 2009 .

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