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Title: The numerical solution of fractional and distributed order differential equations
Author: Connolly, Joseph Arthur
Awarding Body: University of Liverpool
Current Institution: University of Chester
Date of Award: 2004
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Fractional Calculus can be thought of as a generalisation of conventional calculus in the sense that it extends the concept of a derivative (integral) to include non-integer orders. Effective mathematical modelling using Fractional Differential Equations (FDEs) requires the development of reliable flexible numerical methods. The thesis begins by reviewing a selection of numerical methods for the solution of Single-term and Multi-term FDEs. We then present: 1. a graphical technique for comparing the efficiency of numerical methods. We use this to compare Single-term and Multi-term methods and give recommendations for which method is best for any given FDE. 2. a new method for the solution of a non-linear Multi-term Fractional Dif¬ferential Equation. 3. a sequence of methods for the numerical solution of a Distributed Order Differential Equation. 4. a discussion of the problems associated with producing a computer program for obtaining the optimum numerical method for any given FDE.
Supervisor: Ford, Neville J. ; Edwards, John T. Sponsor: Chester College
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: fractional differential equations ; distributed order differential equations ; multi-term fractional differential equations