Abstract
Consider the Caputo fractional $h$-difference equation \[ _a\Delta ^\nu _{h,*}x(t)=c(t)x(t+\nu ), \quad 0\lt \nu \lt 1,\ t\in (h\mathbb{N} )_{a+(1-\nu )h}, \] where $_a\Delta ^\nu _{h,*}x(t)$ denotes the Caputo-like delta fractional $h$-difference of $x(t)$ on sets $(h\mathbb{N} )_{a+(1-\nu )h}$. Our main results are found in Theorems A and B in Section 1. In Section 3, we show that the proof of a recent result in Baleanu, Wu, Bai and Chen is incorrect. Finally, four numerical examples are given to illustrate the main results.
Citation
Baoguo Jia. Xiang Liu. Feifei Du. Mei Wang. "The solution of a new Caputo-like fractional $h$-difference equation." Rocky Mountain J. Math. 48 (5) 1607 - 1630, 2018. https://doi.org/10.1216/RMJ-2018-48-5-1607
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