THE DYNAMICS OF POSITIVE SOLUTIONS OF A HIGHER ORDER FRACTIONAL DIFFERENCE EQUATION WITH ARBITRARY POWERS

Gumus, Mehmet | Soykan, Yuksel

The purpose of this paper is to investigate the local asymptotic stability of equilibria, the periodic nature of solutions, the existence of unbounded solutions and the global behavior of solutions of the fractional difference equation x(n+1) = alpha xn-(k+1)/beta+gamma x(n)(p) (k)x(n)(g)-(k+2), n =0,1... where the parameters alpha, beta, gamma; p, q are non-negative numbers and the initial values x - (k + 2), x -(k + 1),..., x-1; x(0) is an element of R+.