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Abstract

The authors of this paper take a fractional calculus approach to the Casagrandi and Rinaldi mathematical model of tourists in an area or country. The tourism model uses an ordinary differential equation to investigate the number of tourists in the area, the quality of natural resources, and the amounts invested in tourist infrastructure. For each scenario in the model, the ordinary differential equations are fractionalized using the Caputo derivative of a function with respect to a specific exponential function. In each example, we incorporate the concept of fractionalization in conjunction with a specific exponential function in order to change the model. As a result, various hypotheses are elicited by allowing some adjustments to the initial parameters. The results are further displayed by plotting Mittag-Leffler function graphs for various parameters and comparing them to the original solutions. The graphs' analysis investigates the behaviour of the modified model's solution; in this study, all modified model solutions are of the Mittag -Leffler form, whereas all original models solve using an exponential function. The assumptions and changes in parameters cause minor changes in the behaviour of the solutions.