Progress in Fractional Differentiation & Applications

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In this article, a mathematical model for exchange rate movements is derived by applying random walks theory and involving Caputo fractional derivative operator. The waiting time distributions for the exchange rate movement of US Dollar to Japanese Yen, which are intimately related to the mathematical model, during February 2019 are also studied. Three types of waiting time distributions, i.e., exponential, stretched exponential, and Mittag-Leffler distributions are compared. The result shows that Mittag-Leffler Distribution is the best distribution to approximate the empirical distribution of the exchange rate data during February 2019 except the data of February 18, 2019 which is approximated better by stretched exponential distribution.

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