### Analysis of rubella disease model with non-local and non-singular fractional derivatives

Ilknur Koca

#### Abstract

In this paper we investigate a possible applicability of the newly established fractional differentiation in the field of epidemiology. To do this we extend the model describing the Rubella spread by replacing the time derivative with the time fractional derivative for the inclusion of memory. Detailed analysis of existence and uniqueness of exact solution is presented using the Banach fixed point theorem. Finally some numerical simulations are showed to underpin the effectiveness of the used derivative.

#### Keywords

rubella disease model, special solution, fixed point theorem, numerical simulations

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DOI: http://dx.doi.org/10.11121/ijocta.01.2018.00532

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