Accepted for publication in JNEEA

Existence and uniqueness of solution of fractional order nonautonomous neutral differential equation with deviated arguments

M. Malik, S. Abbas, A. Kumar

School of Basic Sciences, Indian Institute of Technology, Mandi, 175001, H.P., INDIA.

Received on June 29, 2016
Accepted on April 12, 2017

Communicated by Gaston M. N'Guérékata

Abstract.  In this paper we discuss the existence and uniqueness of solutions for fractional order neutral differential equation with deviated arguments.We use the method of resolvent operators for integral equations suggested by Hernández et al. (On recent developments in the theory of abstract differential equations with fractional derivatives, Nonlinear Anal. 73 (2010), 3462) for fractional differential equations. At the end an example is given to illustrate our analytical findings.
Keywords: Abstract differential equation; Fractional derivative; Deviated argument; Resolvent operator..
2010 Mathematics Subject Classification:   34K30; 34K37; 47A10.

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