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The Craft of Fractional Modelling in Science and Engineering: II and III

Department of Chemical Engineering, University of Chemical Technology and Metallurgy, 8 Kliment Ohridsky Blvd, 1756 Sofia, Bulgaria
Fractal Fract. 2021, 5(4), 281;
Submission received: 14 December 2021 / Accepted: 16 December 2021 / Published: 20 December 2021
(This article belongs to the Special Issue The Craft of Fractional Modelling in Science and Engineering III)
A comprehensive understanding of fractional systems plays a pivotal role in practical applications. To efficiently exploit all possible engineering applications of fractional-order systems, open problems in this field have to be addressed by offering novel practical and theoretical approaches focused on the modeling, simulation, and control of these systems. In this way, the collection of articles listed below aims to explore recent trends and developments in the modeling, analysis, and synchronization of fractional-order systems. Precisely, we cover a collection of articles published in two Special Issues of Fractal and Fractional.
The Craft of Fractional Modelling in Science and Engineering: II and III, from 2018 till 2021.
The 11 articles span broad aspects of fractional calculus applications to model fundamental issues related to Fix-Write and Gamma functions [1,2], non-Gaussian distributions to random walk in the context of memory [3], comb models with non-static stochastic resetting, and anomalous diffusion [3,4], diffusion and wave propagation in fractional Jeffrey’s-type heat conduction equation [5], and inverse problems in model identifications [6,7].
Real-world problems such as underground water filtration [8,9], fractional electronic elements [10], and viscous thermal losses in musical instruments (flutes) [11] show the power of fractional modelling in modeling complex phenomena with non-locality and energy dissipation.
We believe that this collection of articles will serve as a comprehensive source of information both in problem solving and many new ideas in the amazing field of fractional modelling.
The efforts and contributions of all authors are highly appreciated due to their collaborations in manuscript preparations and the quality of the results reported in them, as well.
Last but not least, the guest editors are indebted to the collaborative work with the editors of Fractal and Fractional in the course of the preparation of this special collection.

Conflicts of Interest

The author declares no conflict of interest.


  1. Prodanov, D. Integral Representations and Algebraic Decompositions of the Fox-Wright Type of Special Functions. Fractal Fract. 2019, 3, 4. [Google Scholar] [CrossRef] [Green Version]
  2. Prodanov, D. Regularized Integral Representations of the Reciprocal Gamma Function. Fractal Fract. 2019, 3, 1. [Google Scholar] [CrossRef] [Green Version]
  3. dos Santos, M.A.F. Non-Gaussian Distributions to Random Walk in the Context of Memory Kernels. Fractal Fract. 2018, 2, 20. [Google Scholar] [CrossRef] [Green Version]
  4. dos Santos, M.A.F. Comb Model with Non-Static Stochastic Resetting and Anomalous Diffusion. Fractal Fract. 2020, 4, 28. [Google Scholar] [CrossRef]
  5. Bazhlekova, E.; Bazhlekov, I. Transition from Diffusion to Wave Propagation in Fractional Jeffreys-Type Heat Conduction Equation. Fractal Fract. 2020, 4, 32. [Google Scholar] [CrossRef]
  6. Brociek, R.; Chmielowska, A.; Słota, D. Parameter Identification in the Two-Dimensional Riesz Space Fractional Diffusion Equation. Fractal Fract. 2020, 4, 39. [Google Scholar] [CrossRef]
  7. Prasad, V.; Kothari, K.; Mehta, U. Parametric Identification of Nonlinear Fractional Hammerstein Models. Fractal Fract. 2020, 4, 2. [Google Scholar] [CrossRef] [Green Version]
  8. Bohaienko, V.; Bulavatsky, V. Mathematical Modeling of Solutes Migration under the Conditions of Groundwater Filtration by the Model with the k-Caputo Fractional Derivative. Fractal Fract. 2018, 2, 28. [Google Scholar] [CrossRef] [Green Version]
  9. Bohaienko, V.; Bulavatsky, V. Simplified Mathematical Model for the Description of Anomalous Migration of Soluble Substances in Vertical Filtration Flow. Fractal Fract. 2020, 4, 20. [Google Scholar] [CrossRef]
  10. Li, M. Power Laws in Fractionally Electronic Elements. Fractal Fract. 2018, 2, 24. [Google Scholar] [CrossRef] [Green Version]
  11. Haidar, G.A.; Moreau, X.; Daou, R.A.Z. Analysis of the Effects of the Viscous Thermal Losses in the Flute Musical Instruments. Fractal Fract. 2021, 5, 11. [Google Scholar] [CrossRef]
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MDPI and ACS Style

Hristov, J. The Craft of Fractional Modelling in Science and Engineering: II and III. Fractal Fract. 2021, 5, 281.

AMA Style

Hristov J. The Craft of Fractional Modelling in Science and Engineering: II and III. Fractal and Fractional. 2021; 5(4):281.

Chicago/Turabian Style

Hristov, Jordan. 2021. "The Craft of Fractional Modelling in Science and Engineering: II and III" Fractal and Fractional 5, no. 4: 281.

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