2016/06/21 by Feifei Du, Baoguo Jia, Lynn Erbe +1 · 1 citation
Mathematics · #Fractional Differential Equations Solutions #Meromorphic and Entire Functions #Nonlinear Differential Equations Analysis
paper · doi:10.1080/10236198.2016.1188089
openalex publication_date 2016/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this paper, we examine the relation between monotonicity and convexity for nabla fractional (q, h)-differences. In particular we prove that Theorem A Theorem A: Assume x:T~(q,h)σ(a)→R, a∇(q,h)αx(t)≥0 for each t∈T~(q,h)σ(a), with 1<α<2. Then ∇(q,h)x(t)≥0 for t∈T~(q,h)σ2(a). Theorem B Theorem B: Assume x:T~(q,h)σ(a)→R, a∇(q,h)αx(t)≥0 for each t∈T~(q,h)σ(a), with 2<α<3. Then ∇(q,h)2x(t)≥0 for t∈T~(q,h)σ3(a). This shows that, in some sense, the positivity of the αth order (q, h)-fractional difference has a strong connection to the monotonicity and convexity of x(t).