In this Article, we observe the Logistic--Map Ansatz, which is a popular
forecasting Model to estimate the Market Penetration of new technologies in
Time evolution. Especially we focus on the Substitution Process of regenerative
resources for electro-energy in B.R.D. as a Case Study using real available
Data. The Aim of this Article is to develop some specific Models that could
represent Logistic Growth implying explicitly the Fractality as the
Substitution Dynamics is characterized by high Complexity and fractal
Characteristics. According to this Target, we consider a specific Fokker-Planck
Ansatz, which could represent the time-fractional Evolution of the Substitution
Grade. Further, we implement a relaxation Model, which focuses on the time
Evolution of the Expected Value of the Substitution Grade. Additionally, a
time-discrete Hybrid model is proposed and a concrete Application of Homotopy
Methode delivers interesting Results.
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