On Riemann and Caputo fractional differences

In this paper, we define left and right Caputo fractional sums and differences, study some of their properties and then relate them to Riemann–Liouville ones studied before by Miller K. S. and Ross B., Atıcı F.M. and Eloe P. W., Abdeljawad T. and Baleanu D., and a few others. Also, the discrete vers...

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Bibliographic Details
Published in:	Computers & mathematics with applications (1987) Vol. 62; no. 3; pp. 1602 - 1611
Main Author:	Abdeljawad, Thabet
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 01.08.2011
Subjects:	Caputo left and right fractional differences Difference equations Discrete Mittag-Leffler function Left and right Riemann differences Left fractional sum Mathematical analysis Mathematical models Right fractional sum Sums Caputo left and right fractional differences Left fractional sum Discrete Mittag-Leffler function Right fractional sum Left and right Riemann differences
ISSN:	0898-1221, 1873-7668
Online Access:	Get full text
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Summary:	In this paper, we define left and right Caputo fractional sums and differences, study some of their properties and then relate them to Riemann–Liouville ones studied before by Miller K. S. and Ross B., Atıcı F.M. and Eloe P. W., Abdeljawad T. and Baleanu D., and a few others. Also, the discrete version of the Q -operator is used to relate the left and right Caputo fractional differences. A Caputo fractional difference equation is solved. The solution proposes discrete versions of Mittag-Leffler functions.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
ISSN:	0898-1221 1873-7668
DOI:	10.1016/j.camwa.2011.03.036