Date Approved

12-15-2000

Embargo Period

6-16-2016

Document Type

Thesis

Degree Name

M.A. in Mathematics

Department

Mathematics

College

College of Science & Mathematics

First Advisor

Wright, Marcus W.

Subject(s)

Fractional calculus

Disciplines

Mathematics

Abstract

In this thesis, the reader will not find a study of any kind; there is no methodology, questionnaire, interview, test, or data analysis. This thesis is simply a research paper on fractional derivatives, a topic that I have found to be fascinating. The reader should be delighted by a short history of the topic in Chapter 1, where he/she will read about the contributions made by some of the great mathematicians from the last three centuries.

In Chapter 2 the reader will find an intuitive approach for finding the general fractional derivative for functions such as eax, xp, and f(x). Other topics in Chapter 2 include branch lines and the Weyl Transform. All of the work preformed by an intuitive approach is backed up by a rigorous approach using Complex Analysis in Chapter 3. In Chapter 4 the reader will find an excellent application of fractional derivatives in solving the tautochrone problem.

No paper on fractional derivatives could be complete with out a chapter (5) on Oliver Heaviside. Heaviside's thoughts on rigorous formalism and his use of non-logical mathematics should delight the reader.

Lastly, the reader should enjoy my final thoughts on this topic as well as Heaviside's thoughts.

Included in

Mathematics Commons

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