Title: Population dynamic caused by war involvement via fractional derivative on time scales

Authors: Mehdi Nategh; Dumitru Baleanu; Abdolali Neamaty; Bahram Agheli

Addresses: Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla Mo, 65401, USA ' Department of Mathematics, Çankaya University, Ankara, 06790, Turkey ' Department of Mathematics, University of Mazandaran, P.O. Box 47416-95447, Pasdaran Street, Babolsar 47416-95447, Iran ' Department of Mathematics, Qaemshahr Branch, Islamic Azad University, P.O. Box 163, Qaemshahr 163, Iran

Abstract: This work suggests a model for a population dynamic caused by an enemy attack to a domain of residential areas. With the help of a local non-integer order rate of change and a new structure induced on the real line, we derive a spatial discrete diffusion equation of fractional order. Then making use of the d'Alembert's change of variable we obtain a time scale which is made of union of disjoint compact intervals. These considerations lead us to a non-homogeneous second order nonlinear differential equation. The existence of a positive solution is discussed and through a numerical example the theory is illustrated.

Keywords: local fractional dynamic; population dynamic; time scales; war involvement.

DOI: 10.1504/IJDSDE.2019.101215

International Journal of Dynamical Systems and Differential Equations, 2019 Vol.9 No.3, pp.213 - 224

Received: 04 May 2017
Accepted: 04 Jan 2018

Published online: 29 Jul 2019 *

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