M.A. in Mathematics
College of Science & Mathematics
Wright, Marcus W.
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.
Beach, John M., "Fractional derivatives" (2000). Theses and Dissertations. 1630.