IJPAM: Volume 89, No. 5 (2013)

OSCILLATION OF CAPUTO LIKE
DISCRETE FRACTIONAL EQUATIONS

S. Lourdu Marian$^1$, M. Reni Sagayaraj$^2$,
A. George Maria Selvam$^3$, M. Paul Loganathan$^4$
$^1$Rajiv Gandhi College of Engineering
Chennai, 105, INDIA
$^{2,3}$Sacred Heart College
Tirupattur, 635 601, INDIA
$^4$Department of Mathematics
Dravidian University
Kuppam, INDIA


Abstract. This paper deals with some oscillation criteria of forced nonlinear fractional difference equations of the form \begin{equation*}
\Delta^{\alpha}_{*} x(t)-g(t+\alpha-1,x(t+\alpha-1))+ f_1(t+\alpha-1,x(t+\alpha-1))= v(t),
\end{equation*}
\begin{multline*}
\Delta^{\alpha}_{*} x(t)-g(t+\alpha-1,x(t+\alpha-1))+ f_1(t+\alpha-1,x(t+\alpha-1))\\ +f_2(t+\alpha-1,x(t+\alpha-1))= v(t)
\end{multline*}
where $\Delta^\alpha_{*}$ is a Caputo like discrete fractional difference operator, $t\in N_{1-\alpha}$, $ 0<\alpha\leq1$, $x(0)= x_0$. $g,f_i:[0,+\infty)\times R\rightarrow R$, $i=1,2$ and $v:[0,+\infty)\rightarrow R$ are continuous with respect $t$ and $x$ and $N_{1-\alpha}=\{1-\alpha, 2-\alpha,\ldots\}$.

Received: August 5, 2013

AMS Subject Classification: 26A33, 39A11, 39A12

Key Words and Phrases: caputo derivative, oscillation, fractional difference equations

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DOI: 10.12732/ijpam.v89i5.3 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 89
Issue: 5