Long time behavior for a nonlinear fractional model

The asymptotic behavior for solutions of a weighted Cauchy-type nonlinear fractional problem is investigated. We find bounds for solutions on infinite time intervals and also provide sufficient conditions assuring decay to zero. This work improves earlier results by the same authors.

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

[2]  N. Tatar,et al.  Global existence and stability of some semilinear problems , 2000 .

[3]  Olof J. Staffans,et al.  Volterra Integral and Functional Equations: Index , 1990 .

[4]  Maria Meehan,et al.  Existence Theory for Nonlinear Integral and Integrodifferential Equations , 1998 .

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

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

[7]  N. Tatar,et al.  Convergence Rates for a Reaction-Diffusion System , 2001 .

[8]  J. Trujillo,et al.  EXISTENCE AND UNIQUENESS THEOREMS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS , 2000 .

[9]  Marek W. Michalski Derivatives of noninteger order and their applications , 1993 .

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

[11]  Kolmanovskii,et al.  Introduction to the Theory and Applications of Functional Differential Equations , 1999 .

[12]  N. Azbelev,et al.  Introduction to the Theory of Linear Functional Differential Equations , 1995 .

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

[14]  Nasser-eddine Tatar,et al.  Power-type estimates for a nonlinear fractional differential equation , 2005 .

[15]  T. A. Burton,et al.  Volterra integral and differential equations , 1983 .

[16]  J. Trujillo,et al.  Differential equations of fractional order:methods results and problem —I , 2001 .

[17]  Milan Medveď,et al.  A New Approach to an Analysis of Henry Type Integral Inequalities and Their Bihari Type Versions , 1997 .

[18]  Constantin Corduneanu,et al.  Functional Equations with Causal Operators , 2002 .

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

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