Abstract in English / In this dissertation we apply linear evolution equations to the Newtonian derivative, Caputo
time fractional derivative and $-time fractional derivative. It is notable that the
most utilized fractional order derivatives for modelling true life challenges are Riemann-
Liouville and Caputo fractional derivatives, however these fractional derivatives have
the same weakness of not satisfying the chain rule, which is one of the most important
elements of the match asymptotic method [2, 3, 16]. Furthermore the classical bounded
perturbation theorem associated with Riemann-Liouville and Caputo fractional derivatives
has con rmed not to be in general truthful for these models, particularly for solution
operators of evolution systems of a derivative with fractional parameter ' that
is less than one (0 < ' < 1) [29]. To solve this problem, we introduce the derivative
with new parameter, which is de ned as a local derivative but has a fractional order
called $-derivative and apply this derivative to linear evolution equation and to support
what we have done in the theory, we utilize application to population dynamics and we provide the numerical simulations for particular cases. / Mathematical Sciences / M.Sc. (Applied Mathematics)
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:unisa/oai:uir.unisa.ac.za:10500/26794 |
| Date | 01 1900 |
| Creators | Monyayi, Victor Tebogo |
| Contributors | Doungmo Goufo, Emile Franc |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
| Format | 1 online resource (74 leaves) : illustrations, application/pdf |
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