TY - JOUR

T1 - Analytical and Numerical Monotonicity Analyses for Discrete Delta Fractional Operators

AU - Nonlaopon, Kamsing

AU - Mohammed, Pshtiwan Othman

AU - Hamed, Y. S.

AU - Muhammad, Rebwar Salih

AU - Brzo, Aram Bahroz

AU - Aydi, Hassen

N1 - Funding Information:
Funding: This research was supported by Taif University Researchers Supporting Project (No. TURSP-2020/155), Taif University, Taif, Saudi Arabia, and the National Science, Research and Innovation Fund (NSRF), Thailand.
Funding Information:
Acknowledgments: This research was supported by Taif University Researchers Supporting Project (No. TURSP-2020/155), Taif University, Taif, Saudi Arabia, and the National Science, Research and Innovation Fund (NSRF), Thailand.
Publisher Copyright:
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2022/5/1

Y1 - 2022/5/1

N2 - In this paper, first, we intend to determine the relationship between the sign of () c0 ∆β y (c0 + 1), for 1 < β < 2, and (∆y)(c0 + 1) > 0, in the case we assume that c0 ∆β 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 () c0 ∆β y (z) and (∆y)(z) > 0 (the monotonicity of y), where c0 ∆β 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 c0 ∆β y (z) by means of numerical simulation.

AB - In this paper, first, we intend to determine the relationship between the sign of () c0 ∆β y (c0 + 1), for 1 < β < 2, and (∆y)(c0 + 1) > 0, in the case we assume that c0 ∆β 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 () c0 ∆β y (z) and (∆y)(z) > 0 (the monotonicity of y), where c0 ∆β 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 c0 ∆β y (z) by means of numerical simulation.

KW - delta fractional difference

KW - discrete fractional calculus

KW - monotonicity

KW - numerical approximation

UR - http://www.scopus.com/inward/record.url?scp=85130866418&partnerID=8YFLogxK

U2 - 10.3390/math10101753

DO - 10.3390/math10101753

M3 - Article

AN - SCOPUS:85130866418

SN - 2227-7390

VL - 10

JO - Mathematics

JF - Mathematics

IS - 10

M1 - 1753

ER -