Comparison theorems and asymptotic behavior of solutions of discrete fractional equations
By Baoguo Jia, Lynn Erbe, Allan Peterson. 2015
48 citations recorded by the source corpus.
Consider the following n-th order nabla and delta fractional difference equa- tions r n(a) x(t) = c(t)x(t), t2 Na+1, x(a) > 0. ( ) We establish comparison theorems by which we compare the solutions x(t) of ( ) and ( ) with the solutions of the equations r n(a) x(t) = bx(t) and D n+n 1 x(t) = bx(t + n 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), 353-370). These results show that the solutions of two fractional difference equationsr n(a) x(t) = cx(t), 0 < n < 1, and D n+n 1 x(t) = cx(t + n 1), 0 < n < 1, have similar asymptotic behavior with the solutions of the first order difference equationsrx(t) = cx(t),jcj < 1 and Dx(t) = cx(t),jcj < 1, respectively.
Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/f9cde3d2019f74398e55dd5c1b20408e8600026a
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In Applied Mathematics
In Modeling and Simulation
In Numerical Analysis
Citations in the corpus
- Asymptotic stability of fractional difference equations with bounded time delays (2020, background): “2 and Theorem B in [17], the following lemma can be acquired.”