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2018 The solution of a new Caputo-like fractional $h$-difference equation
Baoguo Jia, Xiang Liu, Feifei Du, Mei Wang
Rocky Mountain J. Math. 48(5): 1607-1630 (2018). DOI: 10.1216/RMJ-2018-48-5-1607

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

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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

Information

Published: 2018
First available in Project Euclid: 19 October 2018

zbMATH: 06958794
MathSciNet: MR3866561
Digital Object Identifier: 10.1216/RMJ-2018-48-5-1607

Subjects:
Primary: 39A12, 39A70

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 5 • 2018
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