Abstract
In this study, we develop multiple power nonlinear generalizations of Gronwall-Bellman type fractional discrete inequalities and fractional sum inequalities through combining functions with powered unknown functions.We have employed technique of reducing power non-linearity into linearity to furnish these refinements. These novel findings present a broader framework for dealing with wider range of nonlinear fractional difference equations and fractional sum-difference equations. The utilization of these inequalities enables to study certain crucial classes of fractional difference equations that arise in the realm of fractional difference calculus, both quantitatively and qualitatively. Several illustrations are provided to examine the boundedness of initial value problems of fractional difference equations, demonstrating the reliability and effectiveness of our findings.
Recommended Citation
Kendre, Subhash; Kale, Nagesh; and Chalishajar, Dimplekumar
(2025).
(SI14-12) Some Novel Fractional Discrete Inequalities of Gronwall-Bellman Type and Their Applications to Fractional Difference Equations,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 20,
Iss.
3, Article 2.
Available at:
https://digitalcommons.pvamu.edu/aam/vol20/iss3/2
