THE ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF DISCRETE NONLINEAR FRACTIONAL EQUATIONS - Bayram, Mustafa; Secer, Aydin; Adiguzel, Hakan (SPRINGERNATURE, 2020)
In this study, we consider a class of nonlinear fractional difference equa- tions following form: Delta (a(t) g(Delta(alpha)x(t))) + F (t, Sigma(s+t0) (t-1+alpha) (t - s - 1)((-alpha)) x (s) ) =0, where t is an element of Nt(0) + 1-alpha and Delta(alpha) denotes the Riemann-Liouville fractional difference operator of order alpha. Using the generalized Riccati function, we obtain some oscillation criteria. Finally, we give some illustrative examples.
Keywords: fractional calculus; fractional difference equation; oscillation; nonlinear; difference equations; oscillation criteria; EXISTENCE; STABILITY; Mathematics