J. Nonl. Evol. Equ. Appl. 2015 (2), pp. 21-30, published on May 8, 2015:

Asymptotic Behavior of Solutions to Nonlinear Nonlocal Fractional Functional Differential Equations


M. Sharma, S. Dubey

Department of Mathematics; Indian Institute of Technology Madras; Chennai-600 036, India

Received on July 30, 2014, Revised version: October 3, 2014
Accepted on December 15, 2014

Communicated by Gaston M. N'Guérékata

Abstract.  We investigate a nonlinear nonlocal fractional functional differential equations in a Banachspace associated with the family of linear closed operators {−A(t) : t ≥ 0}. The object of ourstudy is to determine the asymptotic behavior of solutions. Also, we render criteria for stability of zero solution. We establish our results with the assumption that −A(t) generates a resolvent operator for each t ≥ 0 and the nonlinear part is continuous in all variables with some certain conditions. We conclude the article with an application of the developed results in which we discuss a nonlocal nonlinear partial fractional functional differential equation.
Keywords:Functional differential equations, fractional calculus, analytic semigroup, resolvent operator.
2010 Mathematics Subject Classification:   26A33, 34A08, 34A12, 34K37, 35B40, 35R11.

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