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 - 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 -