OSCILLATION CRITERIA OF A CLASS OF FRACTIONAL
ORDER DAMPED DIFFERENCE EQUATIONS
A. George Maria Selvam1, R. Janagaraj1
1PG&Research Department of Mathematics
Sacred Heart College (Autonomous)
Tirupattur-635601, Vellore Dt., Tamil Nadu, S. INDIA

Abstract

Herein, we examine the oscillatory behavior of all solutions of a fractional order difference equations with damping term of the form

\begin{displaymath} \Delta^{1+\alpha}u(t)+p(t)\Delta^\alpha u(t)+q(t)F[G(t)]=0, \ \ t\geq t_0>0, \end{displaymath}

where $G(t)=\sum\limits_{s=t_0}^{t-1+\alpha}\left(t-s-1\right)^{-\alpha}u(s)$ and $\Delta^\alpha$ denotes the Riemann-Liouville difference operator of order $0<\alpha\leq 1$. We arrive at some new sufficient conditions for the oscillation of solutions of fractional order damped difference equations using generalized riccati type transformation technique under suitable conditions.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 32
Issue: 3
Year: 2019

DOI: 10.12732/ijam.v32i3.5

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