## Abstract

In this paper, first, we intend to determine the relationship between the sign of () c_{0} ∆^{β} y (c_{0} + 1), for 1 < β < 2, and (∆y)(c_{0} + 1) > 0, in the case we assume that c_{0} ∆^{β} y (c_{0} + 1) is negative. After that, by considering the set D_{ℓ+1,θ} ⊆ D_{ℓ,θ}, which are (subsets) of (1, 2), we will extend our previous result to make the relationship between the sign of () c_{0} ∆^{β} y (z) and (∆y)(z) > 0 (the monotonicity of y), where c_{0} ∆^{β} y (z) will be assumed to be negative for each z ∈ Nc^{T}_{0}:= {c_{0}, c_{0} + 1, c_{0} + 2, …, T} and some T ∈ N_{c0}:= {c_{0}, c_{0} + 1, c_{0} + 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 c_{0} ∆^{β} y (z) by means of numerical simulation.

Original language | English |
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Article number | 1753 |

Journal | Mathematics |

Volume | 10 |

Issue number | 10 |

DOIs | |

Publication status | Published - 1 May 2022 |

Externally published | Yes |

## Keywords

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