This article reveals a specific category of solutions for the 1+1 Variable
Order (VO) nonlinear fractional Fokker-Planck equations. These solutions are
formulated using VO q-Gaussian functions, granting them significant
versatility in their application to various real-world systems, such as
financial economy areas spanning from conventional stock markets to
cryptocurrencies. The VO q-Gaussian functions provide a more robust
expression for the distribution function of price returns in real-world
systems. Additionally, we analyzed the temporal evolution of the anomalous
characteristic exponents derived from our study, which are associated with the
long-range memory in time series data and autocorrelation patterns.Comment: 15 Pages, 3 Figures. Submitted to Physical Review