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 noninteger 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 wellknown integer firstorder and secondorder derivatives are given by f'(t)=x and f''(t)=1, respectively. But how could one compute for example the 1/2th 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:  https://fse.studenttheses.ub.rug.nl/id/eprint/13478 
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