Oscillation of solutions for a class of nonlinear fractional difference equations

Volume 9, Issue 11, pp 5862--5869 http://dx.doi.org/10.22436/jnsa.009.11.14

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Authors

Aydin Secer - Departmet of Mathematical Engineering, Yildiz Technical University, Istanbul, Turkey. Hakan Adiguzel - Institute of science, Yildiz Technical University, Istanbul, Turkey.

Abstract

In this paper, we investigate the oscillation of the following nonlinear fractional difference equations, \[\Delta(a (t) [\Delta(r (t) (\Delta^\alpha x (t))^{\gamma_1} )] ^{\gamma_2}) + q (t) f (\Sigma^{t-1+\alpha}_{s=t_0} (t - s - 1)^{(-\alpha)} x (s) )= 0,\] where \(t \in N_{t_0+1-\alpha},\gamma_1\) and \(\gamma_2\) are the quotient of two odd positive number, and \(\Delta^\alpha\) denotes the Riemann- Liouville fractional difference operator of order \(0 < \alpha\leq 1\).

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Keywords

• Fractional order
• fractional difference equation
• oscillation
• nonlinear
• difference equations
• oscillatory solutions.

MSC

•  39A21
•  39A10
•  26A33

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