Analytical and Numerical Monotonicity Analyses for Discrete Delta Fractional Operators

Abstract

In this paper, first, we intend to determine the relationship between the sign of Δc0βy(c0+1), for 1<β<2, and Δy(c0+1)>0, in the case we assume that Δc0βy(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 Δc0βy(z) and Δy(z)>0 (the monotonicity of y), where Δc0βy(z) will be assumed to be negative for each z∈Nc0T:={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 Δc0βy(z) by means of numerical simulation.