Journal of Mathematical Sciences: Advances and Applications Volume 54, 2018, Pages 25-53 Available at http://scientificadvances.co.in DOI: http://dx.doi.org/10.18642/jmsaa_7100122025 2010 Mathematics Subject Classification: 39A10. Keywords and phrases: asymptotic stability, global convergence, periodic solution, local stability, rational difference equation. Received November 29, 2018; Revised February 09, 2019  2018 Scientific Advances Publishers GLOBAL DYNAMICS OF SOME FRACTIONAL DIFFERENCE EQUATIONS H. EL-METWALLY 1 , E. M. ELABBASY 1 and M. AL-KAFF 2 1 Department of Mathematics Faculty of Science Mansoura University Mansoura 35516 Egypt e-mail: eaash69@yahoo.com emelabbasy@mans.edu.eg 2 Department of Mathematics Hadhramout University Yemen e-mail: abohassien246@gmail.com Abstract We investigate the global dynamics of the equation , , 1 , 0 , 1 1 2 1 1 … = γ + β + α = − − − + n x x x x x x n n n n n n where the parameters , , β α and γ are nonnegative numbers with 0 > γ + β + α and the initial conditions 1 − x and 0 x are arbitrary positive real numbers. The equilibrium points of the considered equation are obtained and