A fractional-order model of the dynamics of the electorate in a multi-party democracy

Abstract

The complexity of real-world problems has led to the development of fractional differential operators, a groundbreaking mathematical tool that overcomes the limitations of classical calculus. This article proposes an ABC fractional derivative model to analyze the dynamics of the electorate in multiparty democracies. The ABC fractional derivatives, characterized by their non-local and non-singular kernels, facilitate a deeper understanding of the crossover behavior in the model, yielding valuable insights into the complex underlying dynamics. The properties of the Atangana–Baleanu operator are explored, and the uniqueness and existence of solutions are determined. The Hyers–Ulam stability is established, and the political party reproduction is calculated. The model is validated using data from the 2020 Ghana Presidential Elections, exhibiting a crossover effect at $\xi =0.2.$ The fractional order operator significantly impacts all compartments, predicting an increase in votes for small parties and a decline for major parties. In particular, the findings reveal a significant increase in voters who joined political parties in the past four years. Future studies may explore optimal control strategies for multiparty democracies.