Population dynamic caused by war involvement via fractional derivative on time scales
by Mehdi Nategh; Dumitru Baleanu; Abdolali Neamaty; Bahram Agheli
International Journal of Dynamical Systems and Differential Equations (IJDSDE), Vol. 9, No. 3, 2019

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.

Online publication date: Mon, 29-Jul-2019

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