Fractional-order dynamical model for electricity markets

In this article, we use a generalized system of differential equations of fractional-order to incorporate memory into an electricity market model. By using this idea, essential information from the past, such as the behavior of market participants, namely, suppliers and consumers, can be used and have impact on future decisions. We construct the fractional-order dynamical model, study its solutions, and provide closed formulas of solutions. Finally, we provide an application by using the proposed formula of solutions as well as a numerical example which also compares the proposed model with a conventional, integer-order electricity market model. Results indicate that the inclusion of memory leads market participants to adopt a conservative behavior.