A theoretical investigation of Caputo variable order fractional differential equations: existence, uniqueness, and stability analysis

This paper deals with the analysis of Caputo variable order fractional differential equations. The main objective of the paper is to investigate the existence and uniqueness of solutions to the problem at hand. To achieve this, the paper employs the hypothesis of ordinary differential equations and derives a theorem of continuity for VOFDE. The results of the study show that there is global existence of solutions to the problem under consideration. Furthermore, the paper also establishes results for Caputo variable order FDE and demonstrates Ulam–Hyers stability. This indicates that small changes in initial conditions or parameters of the equation result in small changes in the solution of the equation. Overall, the research paper contributes to the understanding of Caputo variable order fractional differential equations and provides theoretical results that can be useful in various applications.