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Mainardi, F., Luchko, Y., & Pagnini, G. (2001). The Fundamental Solution of the Space-Time Fractional Diffusion Equation. Fractional Calculus and Applied Analysis, 4.

has been cited by the following article:

• TITLE: The Substitution Process for Conventional Energy. The Logistic Map and Some Specific Fractional Aspects

  AUTHORS: Asterios Touplikiotis

  KEYWORDS: Conventional Energy, Regenerative Resources, Logistic Map, Mittag-Leffler Relaxation, Fokker-Planck Ansatz, Homotopy Methode

  JOURNAL NAME: Theoretical Economics Letters, Vol.14 No.1, February 29, 2024

  ABSTRACT: 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.