The planned project is aimed at attempting to construct efficient mathematical models based on the fractional calculus using new machine learning techniques as a tool for identifying parameters. Up to our knowledge, machine learning methods have not yet been adapted to the fractional models. Fractional calculus is a generalization of classical integral and differential calculus. From the point of view of modeling the dynamics of phenomena, the most desirable feature of fractional derivatives is their non-locality. This property is key in modeling systems with so-called "Memory effect" or combining different scales of time and / or space. The fractional calculus also allows to reduce the parameters needed to describe the studied phenomenon. The project will focus on two issues where the use of fractional calculus along with new parameter identification methods can have a significant impact on improving the quality of modeling: construction of a mathematically well-established high-throughput model of Dengue virus spread that takes into account the 'memory effect' of the mosquito population; the use of fractional calculus for modeling electrical machines, which will reduce the dimension of the model equations and / or parameters and keep their values constant. It is planned to: obtain a high-performance model with a sufficient number of parameters for its identification; providing a clear relationship between the model parameters and the data from the problem characteristics; constructing a numerical method for simulating the obtained model, which respects the fundamental properties of the problem; developing optimization methods based on new machine learning methods. The research internship will take place at the University of Pau with prof. Jacky Cresson. Professor Cresson is a recognized expert in the field of fractional calculus and dynamical systems. The work on parameter identification using machine learning methods will be carried out in collaboration with Sebastien Loustau, who is an expert in deep learning and machine learning. The result of the research stay at LMAP will be the increase of the applicant's knowledge in the field of fractional calculus, dynamical systems and optimization methods. This will deepen and extend cooperation with a strong foreign research center LMAP, which will result in submitting an application for an international grant in the form of Polish-French scientific cooperation.