Off-campus UNL users: To download campus access dissertations, please use the following link to log into our proxy server with your NU ID and password. When you are done browsing please remember to return to this page and log out.
Non-UNL users: Please talk to your librarian about requesting this dissertation through interlibrary loan.
Sequential Differences in Nabla Fractional Calculus
Abstract
We study the composition of nabla fractional differences of unequal orders, known as "sequential" nabla fractional differences. The sequential differences we examine possess different bases — specifically, we establish the outer operator as having a base larger than the inner operator by at least an integer factor of 1. Further, we consider two cases of orders: first the case when the outer difference has a larger power, and second when the inner difference has a larger power. In this work, we develop rules for sequential nabla fractional differences and present connections between the sign of a sequential difference of a function and the monotonicity of that function. We establish uniqueness of solutions to various initial value problems and boundary value problems involving sequential nabla fractional differences and give an explicit expression for the Green's functions. We investigate properties of the Green's functions and explore some useful generalizations involving sequential nabla fractional differences.
Subject Area
Mathematics
Recommended Citation
Setniker, Ariel, "Sequential Differences in Nabla Fractional Calculus" (2019). ETD collection for University of Nebraska-Lincoln. AAI13861982.
https://digitalcommons.unl.edu/dissertations/AAI13861982