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.

Boundary value problems for discrete fractional equations

Pushp Awasthi, University of Nebraska - Lincoln

Abstract

In this dissertation we develop certain aspects of the theory of discrete fractional calculus. The author begins with an introduction to the discrete delta calculus together with the fractional delta calculus which is used throughout this dissertation. The Cauchy function, the Green's function and some of their important properties for a fractional boundary value problem are developed. This dissertation is comprised of four chapters. In the first chapter we introduce the delta fractional calculus. In the second chapter we give some preliminary definitions, properties and theorems for the fractional delta calculus and derive the appropriate Green's function and give some of its important properties. This allows us to prove some important theorems by using well-known fixed point theorems. In the third chapter we study and prove various results regarding a so-called self-adjoint equation with Sturm-Liouville type boundary conditions. In the fourth chapter we prove some theorems regarding the existence and uniqueness of positive solution of a forced fractional equation with finite limit.^

Subject Area

Applied Mathematics|Mathematics|Theoretical Mathematics

Recommended Citation

Awasthi, Pushp, "Boundary value problems for discrete fractional equations" (2013). ETD collection for University of Nebraska - Lincoln. AAI3564139.
http://digitalcommons.unl.edu/dissertations/AAI3564139

Share

COinS