Rocky Mountain Journal of Mathematics

The solution of a new Caputo-like fractional $h$-difference equation

Baoguo Jia, Xiang Liu, Feifei Du, and Mei Wang

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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.

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Rocky Mountain J. Math., Volume 48, Number 5 (2018), 1607-1630.

First available in Project Euclid: 19 October 2018

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Zentralblatt MATH identifier

Primary: 39A12: Discrete version of topics in analysis 39A70: Difference operators [See also 47B39]

Caputo $h$-fractional difference Mittag-Leffler function power rule


Jia, Baoguo; Liu, Xiang; Du, Feifei; Wang, Mei. The solution of a new Caputo-like fractional $h$-difference equation. Rocky Mountain J. Math. 48 (2018), no. 5, 1607--1630. doi:10.1216/RMJ-2018-48-5-1607.

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