Analytical and Numerical Monotonicity Analyses for Discrete Delta Fractional Operators

Kamsing Nonlaopon, Pshtiwan Othman Mohammed*, Y. S. Hamed, Rebwar Salih Muhammad, Aram Bahroz Brzo, Hassen Aydi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, first, we intend to determine the relationship between the sign of () c0β y (c0 + 1), for 1 < β < 2, and (∆y)(c0 + 1) > 0, in the case we assume that c0β y (c0 + 1) is negative. After that, by considering the set Dℓ+1,θ ⊆ Dℓ,θ, which are (subsets) of (1, 2), we will extend our previous result to make the relationship between the sign of () c0β y (z) and (∆y)(z) > 0 (the monotonicity of y), where c0β y (z) will be assumed to be negative for each z ∈ NcT0:= {c0, c0 + 1, c0 + 2, …, T} and some T ∈ Nc0:= {c0, c0 + 1, c0 + 2, … }. The last part of this work is devoted to see(the possibility) of information reduction regarding the monotonicity of y despite the non-positivity of c0β y (z) by means of numerical simulation.

Original languageEnglish
Article number1753
JournalMathematics
Volume10
Issue number10
DOIs
Publication statusPublished - 1 May 2022
Externally publishedYes

Keywords

  • delta fractional difference
  • discrete fractional calculus
  • monotonicity
  • numerical approximation

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