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Comparison Theorems And Asymptotic Behavior Of Solutions Of Discrete Fractional Equations, Baoguo Jia, Lynn Erbe, Allan Peterson
Comparison Theorems And Asymptotic Behavior Of Solutions Of Discrete Fractional Equations, Baoguo Jia, Lynn Erbe, Allan Peterson
Department of Mathematics: Faculty Publications
Consider the following n-th order nabla and delta fractional difference equations
rn r (a)x(t) = c(t)x(t), t 2 Na+1, x(a) > 0.
and
Va+v-1x(t) = c(t)x(t + v - 1), t 2 Na, x(a + n - 1) > 0
We establish comparison theorems by which we compare the solutions x(t) of (*) and (**) with the solutions of the equations rn r(a)x(t) = bx(t) and Dn a+v-1x(t) = bx(t + v -1), respectively, where b is a constant. We obtain four asymptotic results, one of them extends the recent result [F. M. Atici, P. W. Eloe, Rocky Mountain J. Math. 41(2011), …