Journal of Environmental Biology

Generalized population dynamic operator with delay based

on fractional calculus

Rabha W. Ibrahim¹*, M.Z. Ahmad² and M. Jasim Mohammed²

¹Faculty of Computer Science and Information Technology, University, Malaya, 50603, Malaysia

²Institute of Engineering Mathematics, Universiti Malaysia Perlis, 02600 Arau Perlis, Malaysia

*Corresponding Author E-mail: rabhaibrahim@yahoo.com

Publication Data

Paper received:

04 November 2015

Revised received:

27 April 2016

Re-revised received:

05 May 2016

Accepted:

23 June 2016

Abstract

In population dynamics, a growing population consumes more food than a matured one that depends upon condition of individual species. This hints to neutral equations. In the present study, certain sufficient conditions for the existence of periodic solutions to a generalized Rayleigh-type equation with state dependent delay, based on fractional calculus concept was investigated.   

 Key words

Fractional calculus, Fractional differential operator, Fractional differential equation,? Rayleigh equation,? Periodic solution 

Copyright ? 2016 Triveni Enterprises. All rights reserved. No part of the Journal can be reproduced in any form without prior permission. Responsibility regarding the authenticity of the data, and the acceptability of the conclusions enforced or derived, rest completely with the author(s).