Oscillation and asymptotics for damped fractional difference equations
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摘要: 使用广义的Riccati技巧，研究了一类具有阻尼项的分数阶差分方程$\Delta \left\{ {r\left( t \right){{\left[ {{\Delta ^\alpha }y\left( t \right)} \right]}^\gamma }} \right\} + p\left( t \right){\left[ {{\Delta ^\alpha }y\left( t \right)} \right]^\gamma } + q\left( t \right)f\left[ {\sum\nolimits_{s = t0}^{t - 1 + \alpha } {{{\left( {t - s - 1} \right)}^{\left( { - \alpha } \right)}}y\left( s \right)} } \right] = 0 $，t∈ N t0+1-α，得到了其解的振动性的一些新准则.所得的结果改进和推广了某些分数阶离散方程的结果.Abstract: Using generalized Riccati transformation, we investigate the os-cillation of the following fractional difference equations with damping term $\Delta \left\{ {r\left( t \right){{\left[ {{\Delta ^\alpha }y\left( t \right)} \right]}^\gamma }} \right\} + p\left( t \right){\left[ {{\Delta ^\alpha }y\left( t \right)} \right]^\gamma } + q\left( t \right)f\left[ {\sum\nolimits_{s = t0}^{t - 1 + \alpha } {{{\left( {t - s - 1} \right)}^{\left( { - \alpha } \right)}}y\left( s \right)} } \right] = 0 $, t∈ N t0+1-α. Some new oscillation criteria are generalized. The results in this paper extend and improve some known results.
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Key words:
- fractional difference equations /
- damping term /
- oscillation
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