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Fractional Calculus

Koning, D.E. (2015) Fractional Calculus. Bachelor's Thesis, Mathematics.

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Abstract

In this bachelor project we studied Fractional Calculus, the branch of Mathematics which deals with non-integer order integrals and derivatives. These so called fractional integrals and fractional derivatives, or combined ‘differintegrals’, can be of real or complex orders and therefore also include integer orders. For instance, if we consider the function f(t)=1/2x^2 the well-known integer first-order and second-order derivatives are given by f'(t)=x and f''(t)=1, respectively. But how could one compute for example the 1/2-th order derivative or the sqrt(1/2)-th order derivative? We consider two approaches for defining a differintegral and some basic properties, e.g. Linearity, Leibniz’s Rule and composition, will be proved. Furthermore, fractional differential equations and the Laplace Transform method for solving them will be discussed.

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 08:09
Last Modified: 15 Feb 2018 08:09
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/13478

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