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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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.

Article information

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

Dates
First available in Project Euclid: 19 October 2018

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1539936038

Digital Object Identifier
doi:10.1216/RMJ-2018-48-5-1607

Mathematical Reviews number (MathSciNet)
MR3866561

Zentralblatt MATH identifier
06958794

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

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

Citation

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. https://projecteuclid.org/euclid.rmjm/1539936038


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