Caputo type fractional difference operator and its application on discrete time scales

Mohamad Rafi Segi Rahmat, Mohd. Salmi Md. Noorani

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

In this paper, we introduce the analogue of Caputo type fractional derivatives on a (q,h)$(q,h)$-discrete time scale which can be reduced to Caputo type fractional differences studied by Abdeljawad (Comput. Math. Appl. 62:1602-1611, 2011) and Caputo type fractional q-differences studied by Atici and Eloe via the choice q=h=1 and h=0, respectively. Then, we solve linear fractional difference equations involving Caputo type (q,h)-derivatives and give the general solutions in terms of discrete Mittag-Leffler functions introduced by Cermak et al. In addition, we also apply the (q,h)$(q,h)$-Laplace transform method to solve these linear fractional order difference equations.

Original languageEnglish
Article number160
JournalAdvances in Difference Equations
Volume2015
Issue number1
DOIs
Publication statusPublished - 27 Dec 2015

Fingerprint

Difference Operator
Difference equations
Discrete-time
Fractional
Derivatives
Difference equation
Laplace transforms
Mittag-Leffler Function
Fractional Derivative
Linear Order
Fractional Order
General Solution
Laplace transform
Analogue
Derivative

Keywords

  • (q,h)-calculus
  • discrete time scales
  • fractional calculus
  • fractional difference equations

ASJC Scopus subject areas

  • Applied Mathematics
  • Algebra and Number Theory
  • Analysis

Cite this

Caputo type fractional difference operator and its application on discrete time scales. / Segi Rahmat, Mohamad Rafi; Md. Noorani, Mohd. Salmi.

In: Advances in Difference Equations, Vol. 2015, No. 1, 160, 27.12.2015.

Research output: Contribution to journalArticle

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