Differential Equations and Dynamical Systems

, Volume 25, Issue 4, pp 499–517 | Cite as

Analysis of Fractional Functional Differential Equations of Neutral Type with Nonlocal Conditions

Original Research

Abstract

This work deals with the existence of solutions for a class of nonlinear nonlocal fractional functional differential equations of neutral type in Banach spaces. In particular, we prove the existence of solutions with the assumptions that the nonlinear parts satisfy locally Lipschitz like conditions and closed linear operator \(-A(t)\) generates analytic semigroup for each \(t \ge 0\). We also investigate global existence of solution and study the continuous dependence of solution on initial data. We conclude the article with an application to the developed results.

Keywords

Neutral functional differential equations Fractional calculus Analytic semigroup 

Mathematics Subject Classification

26A33 34A08 34A12 34K37 34K40 35A01 35A02 35A09 35R11 

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Copyright information

© Foundation for Scientific Research and Technological Innovation 2016

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology MadrasChennaiIndia

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