### Modeling of Duhem hysteresis with Riemann-Liouville fractional derivative

Beyza Billur İskender Eroğlu

#### Öz

Due to the memory effect of hysteresis, this work considers the fractional order
modeling of hysteresis with singular fractional derivative. For this purpose, the paper focuses on Duhem hysteresis since it is a model defined by a differential equation despite the most of hysteresis models. The model is adapted to a fractional order differential equation in the sense of Riemann-Liouville derivative
and solved by using Grünwald Letnikov approximation. Then, fractional order Duhem model is demonstrated for different order of the derivative by figures drawn using MATLAB. It is observed from the figures that the fractional model exhibits hysteresis behavior for fractional orders smaller than 1.

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