On Riemann and Caputo fractional differences

Thabet Abdeljawad

doi:10.1016/j.camwa.2011.03.036

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$On Riemann and Caputo fractional differences$

Journal article

Peer reviewed

On Riemann and Caputo fractional differences

Thabet Abdeljawad

Computers & mathematics with applications (1987), Vol.62(3), pp.1602-1611

01/08/2011

DOI: https://doi.org/10.1016/j.camwa.2011.03.036

Abstract

Caputo left and right fractional differences

Discrete Mittag-Leffler function

Left and right Riemann differences

Left fractional sum

Right fractional sum

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.

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Details

Title: On Riemann and Caputo fractional differences
Creators - without role: Thabet Abdeljawad - Çankaya University
Publication Details: Computers & mathematics with applications (1987), Vol.62(3), pp.1602-1611
Publisher: Elsevier Ltd
Identifiers: 9926683108331
Academic Unit: Prince Sultan University
Language: English
Resource Type: Journal article