A Study on Advanced Techniques for Fractional Differential Equations: Integrating the Frobenius Method, ZZ Transform, and Diverse Machine Learning Approaches

This study explores fractional differential equations using fractional calculus techniques, extending the traditional Frobenius method with approaches like the ZZ transform and binomial series expansions. It presents efficient techniques for solving such equations and provides examples of their use in problem solving. Also, the study uses machine learning methodologies to solve approximate solutions; it also creates data sets for various fractional differential equations. The study assesses model accuracy by the plots of histograms, scatter plots, box plots, and learning curves. Accordingly, these findings provide an improved comprehension of the capacities of machine learning regarding the solution of such fractional differential equations.