Analytical and Numerical Monotonicity Analyses for Discrete Delta Fractional Operators.

In this paper, first, we intend to determine the relationship between the sign of Δ c 0 β y (c 0 + 1) , for 1 < β < 2 , and Δ y (c 0 + 1) > 0 , in the case we assume that Δ 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 Δ c 0 β y (z) and Δ y (z) > 0 (the monotonicity of y), where Δ c 0 β y (z) will be assumed to be negative for each z ∈ N c 0 T : = { c 0 , c 0 + 1 , c 0 + 2 , ⋯ , T } and some T ∈ N c 0 : = { 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 Δ c 0 β y (z) by means of numerical simulation. [ABSTRACT FROM AUTHOR]