References

1. Mandelbrot, B.B. Stochastic Models for the Earth’s Relief, the Shape and the Fractal Dimension of the Coastlines, and the Number-area Rule for Islands. Proc. Natl. Acad. Sci. USA 1975, 72, 3825–3828.
2. Sun, J.; Ji, Z.; Zhang, Y.; Yu, Q.; Ma, C. A Contact Mechanics Model for Rough Surfaces Based on a New Fractal Characterization Method. Int. J. Appl. Mech. 2018, 10, 1850069.
3. Ma, J.; Liu, D.; Chen, Y. Random Fractal Characters and Length Uncertainty of the Continental Coastline of China. J. Earth Syst. Sci. 2016, 125, 1615–1621.
4. Jiang, Z.-Q.; Xie, W.-J.; Zhou, W.-X.; Sornette, D. Multifractal Analysis of Financial Markets: A Review. Rep. Prog. Phys. 2019, 82.
5. Dimri, V.P.; Ganguli, S.S. Fractal Theory and Its Implication for Acquisition, Processing and Interpretation (API) of Geophysical Investigation: A Review. J. Geol. Soc. India 2019, 93, 142–152.
6. Tang, S.W.; He, Q.; Xiao, S.Y.; Huang, X.Q.; Zhou, L. Fractal Plasmonic Metamaterials: Physics and Applications. Nanotechnol. Rev. 2015, 4, 277–288.
7. Jeldres, R.I.; Fawell, P.D.; Florio, B.J. Population Balance Modelling to Describe the Particle Aggregation Process: A review. Powder Technol. 2018, 326, 190–207.
8. Dan-Ling, W.D.; Juan-Fang, L.I. A Study on the Characteristics of Liquid-vapor Interface by Using Fractal Theory. In Proceedings of the International Symposium on Heat Transfer & Energy Conservation, Guangzhou, China, 11–15 January 2004.
9. Zhou, J.; Sancaktar, E. Yield Behavior of Moderately Filled Epoxy/Ni Suspensions. J. Adhes. Sci. Technol. 2010, 24, 1929–1948.
10. Solov’Yov, I.A.; Solov’Yov, A.V. Simulation of nanofractal dynamics with MBN Explorer. J. Phys. Conf. Ser. 2013, 438, 012006.
11. Santillán, J.M.J.; Van Raap, M.F.; Zélis, P.M.; Coral, D.F.; Muraca, D.; Schinca, D.C.; Scaffardi, L.B. Ag nanoparticles formed by femtosecond pulse laser ablation in water: Self-assembled fractal structures. J. Nanoparticle Res. 2015, 17, 17.
12. Xiao-Xu, L.; Jing-Hua, Y.; Dao-Bin, S.; Wen-Bin, B.; Wei-Dong, C.; Zhong-Hua, W. Small-Angle X-Ray Scattering Study on Nanostructures of Polyimide Films. Chin. Phys. Lett. 2010, 27, 27.
13. Tian, D.; Li, X.; He, J.-H. Self-assembly of macromolecules in a long and narrow tube. Therm. Sci. 2018, 22, 1659–1664.
14. Pandey, I.; Chandra, A. Factors affecting fractal patterns obtained by electroless deposition in polymer. Mater. Res. Express 2019, 6, 105307.
15. Ritter, J.E.; Huseinovic, A. Adhesion and Reliability of Epoxy/Glass Interfaces. J. Electron. Packag. 2000, 123, 401–404.
16. Ji, N.P.; Kaifeng, Z. Fractal Characterization of Uniformity of Discrete Phase in Nanocomposites. J. B. Univ. Aeronaut. Astronaut. 2009, 35, 852–855.
17. Shaoqun, Z.; Jun, H.; Wei, X.; Guangwei, C.; Yangjun, L.; Wei, S.; Jiaxiong, Y. Fracture Features and the Relationship between Wood Shear Strength and Fractal Dimension. Sci. Silvae Sin. 2015, 51, 127–134.
18. Wang, C.; Smith, L.M.; Wang, G.; Shi, S.Q.; Cheng, H.; Zhang, S. Characterization of interfacial interactions in bamboo pulp fiber/high-density polyethylene composites treated by nano CaCO3 impregnation modification using fractal theory and dynamic mechanical analysis. Ind. Crop. Prod. 2019, 141, 111712.
19. Starodubtseva, M.; Starodubtsev, I.E.; Starodubtsev, E.G. Novel fractal characteristic of atomic force microscopy images. Micron 2017, 96, 96–102.
20. Gabibov, I.A.; Dyshin, O.A.; Rustamova, K.B. Formation of the properties of the structure of disperse-filled polymer composites. Plast. Massy 2019, 23–26.
21. Xue, M.G.; Wang, S.F. The Analysis of Relationships between Surface Porosity and Air Permeability of Paper (board). Adv. Mater. Res. 2011, 396–398, 1426–1429.
22. Campano, C.; Balea, A.; Ángeles, B.; Negro, C. A reproducible method to characterize the bulk morphology of cellulose nanocrystals and nanofibers by transmission electron microscopy. Cellulose 2020, 27, 4871–4887.
23. Ferreira, W.H.; Dahmouche, K.; Andrade, C.T. Dispersion of reduced graphene oxide within thermoplastic starch/poly(lactic acid) blends investigated by small-angle X-ray scattering. Carbohydr. Polym. 2019, 208, 124–132.
24. Codou, A.; Misra, M.; Andrzejewski, J. Sustainable biocomposites from Nylon 6 and polypropylene blends and biocarbon—Studies on tailored morphologies and complex composite structures. Compos. Part. A Appl. Sci. Manuf. 2020, 129, 105680.
25. Xian, Y.; Wang, C.; Wang, G.; Smith, L.; Cheng, H. Fractal dimension analysis of interface and impact strength in core–shell structural bamboo plastic composites. Iran. Polym. J. 2017, 26, 169–178.
26. Wei, F.; Wang, W.; Zhang, J. Fractal Characterization of Section Impact Strength of Polypropylene Compound Packaging Materials. Packag. Eng. 2016, 37, 61–65.
27. Zhang, C. Tensile Strength and Fractal Characteristics of SiC Filled PP/FA Composites. Packag. Eng. 2017.
28. Lu, D.R.; He, C.X. Quantitative Analysis of Microcracks in Nano-ALN /PTFE Composites Based on Fractal Theory. In Proceedings of the 10th Sino-Japanese Composite Materials Academic Conference, Chengdu, China, 8 September 2012; pp. 136–139.
29. Chen, Y.; Deng, Z.; Cheng, Q. Thermal conductivity of Si/Ge nanocomposites with fractal tree-shaped networks by considering the phonon interface scattering. Int. J. Heat Mass Transf. 2015, 88, 572–578.
30. Minakova, N.N.; Ushakov, V.Y. Application of Texture Analysis to Assess the Operability of Filled Polymers at High Temperatures. Russ. Phys. J. 2016, 58, 1627–1634.
31. Wu, C.; Liu, C.; Chen, Z.; Liang, J. Fractal Quantitative Characterization of Disperse Effect of Glass Beads in Filled Polypropylene Composites. Eng. Plast. Appl. 2016, 44, 92–97.
32. Zhu, Q.; Zhang, C.; Yang, W. The Influence of permeability on the ablation process for an ablative material. Fractals 2019, 27, 27.
33. Jelčič, Ž.; Holjevac-Grguric, T.; Rek, V. Mechanical properties and fractal morphology of high-impact polystyrene/poly(styrene-b-butadiene-b-styrene) blends. Polym. Degrad. Stab. 2005, 90, 295–302.
34. Devakul, T.; You, Y.; Burnell, F.J.; Sondhi, S. Fractal Symmetric Phases of Matter. SciPost Phys. 2019, 6, 007.
35. Silva, F.; Gonçalves, L.; Fereira, D.; Rebello, J. Characterization of failure mechanism in composite materials through fractal analysis of acoustic emission signals. Chaos Solitons Fractals 2005, 26, 481–494.
36. Zhang, M.; Jiang, M.; Lu, Z.; Liu, G.; Song, S.; Yang, B. Characterization of Structure and Properties of Para-Phenylene Terephthalamide Paper-Based Composites by Fractal Dimension. Polym. Mater. Sci. Eng. 2015, 31, 96–101.
37. Liu, G.; Zhang, M.; Ridgway, C.J.; Gane, P.A.C. Spontaneous Inertial Imbibition in Porous Media Using a Fractal Representation of Pore Wall Rugosity. Transp. Porous Media 2014, 104, 231–251.
38. Jian-Chao, C.; Yu, B.; Mao-Fei, M.; Liang, L. Capillary Rise in a Single Tortuous Capillary. Chin. Phys. Lett. 2010, 27, 054701.
39. Onda, T.; Shibuichi, S.; Satoh, A.N.; Tsujii, K. Super-Water-Repellent Fractal Surfaces. Langmuir 1996, 12, 2125–2127.
40. Cai, J.; Sun, S. Fractal Analysis of Fracture Increasing Spontaneous Imbibition in Porous Media with Gas-Saturated. Int. J. Mod. Phys. C 2013, 24.
41. Xiao, B.; Zhang, X.; Jiang, G.; Long, G.; Wang, W.; Zhang, Y.; Liu, G. Kozeny–Carman constant for gas flow through fibrous porous media by fractal-monte carlo simulations. Fractals 2019, 27, 1950062.
42. Li, X. Research on Porous Media Seepage Based on Directional Random Walking Method. Master’s Thesis, Yangzhou University, Yangzhou, China, 2018.
43. Kosmidis, K.; Macheras, P. On the Dilemma of Fractal or Fractional Kinetics in Drug Release Studies: A Comparison Between Weibull and Mittag-Leffler Functions. Int. J. Pharm. 2018, 543, 269–273.
44. Su, W. Construction of Fractal Calculus. Sci. Sin. Math. 2015, 45, 1587–1598.
45. Aln, Q.T.; He, J.H. On Two-Scale Dimension and Its Applications. Therm Sci. 2019, 23, 1707–1712.
46. Coronel-Escamilla, A.; Gomez-Aguilar, J.F.; Torres, L.; Escobar-Jimenez, R.F. A Numerical Solution for a Variable-Order Reaction-Diffusion Model by Using Fractional Derivatives with Non-Local and Non-Singular Kernel. Phys. A 2018, 491, 406–424.
47. Gomez-Aguilar, J.F. Chaos in a nonlinear Bloch System with Atangana-Baleanu Fractional Derivatives. Numer Meth. Part. D E 2018, 34, 1716–1738.
48. Coronel-Escamilla, A.; Gomez-Aguilar, J.F.; Baleanu, D.; Cordova-Fraga, T.; Escobar-Jimenez, R.F.; Olivares-Peregrino, V.H.; Al Qurashi, M.M. Bateman-Feshbach Tikochinsky and Caldirola-Kanai Oscillators with New Fractional Differentiation. Entropy 2017, 19, 55.
49. Aguilar, J.F.G.; Cordova-Fraga, T.; Torres-Jimenez, J.; Escobar-Jimenez, R.F.; Olivares-Peregrino, V.H.; Guerrero-Ramirez, G.V. Nonlocal Transport Processes and the Fractional Cattaneo-Vernotte Equation. Math. Probl. Eng. 2016, 2016.