Table of Content

Fractal-Fractional Models for Engineering & Sciences

Submission Deadline: 01 October 2022 (closed)

Guest Editors

Prof. JI-Huan He, Soochow University, China
Dr. Muhammad Nadeem, Yibin University, China

Summary

Fractal geometry, two-scale fractal, fractional calculus, discontinuity, fractal MEMS system, fractal vibration system, fractal solitary theory, fractal variational theory.


An engineer is familiar with differential models for complex problems, but they become inaccurate or even invalid for discontinuous problems, e.g., porous medium, stochastic diffusion and permeability. To overcome the shortcoming of the traditional calculus, the fractal theory and fractional calculus have to be adopted.


This special issue focuses on the last development of the fractal-fractional theory for discontinuous problems for applications in engineering & sciences, and submissions on the following specific topics are welcome:

 1) Fractal theory for natural phenomena and meta-materials and other artificial materials;

 2) Fractal theory for mechanical and architectural designs;

 3) Fractal patterns in natural phenomena and chaotic structures;

 4) Fractal-fractional differential models for practical problems

 5)  Physical laws in fractal space or fractal spacetime;

 6) Two-scale economics and two-scale mathematics;

 7) Analytical methods and Numerical methods for fractal–fractional differential equations



Keywords

Fractal geometry, two-scale fractal, fractional calculus, discontinuity, fractal MEMS system, fractal vibration system, fractal solitary theory, fractal variational theory.

Published Papers


  • Open Access

    ARTICLE

    Bifurcation Analysis and Bounded Optical Soliton Solutions of the Biswas-Arshed Model

    Fahad Sameer Alshammari, Md Fazlul Hoque, Harun-Or-Roshid, Muhammad Nadeem
    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2197-2217, 2023, DOI:10.32604/cmes.2023.022301
    (This article belongs to this Special Issue: Fractal-Fractional Models for Engineering & Sciences)
    Abstract We investigate the bounded travelling wave solutions of the Biswas-Arshed model (BAM) including the low group velocity dispersion and excluding the self-phase modulation. We integrate the nonlinear structure of the model to obtain bounded optical solitons which pass through the optical fibers in the non-Kerr media. The bifurcation technique of the dynamical system is used to achieve the parameter bifurcation sets and split the parameter space into various areas which correspond to different phase portraits. All bounded optical solitons and bounded periodic wave solutions are identified and derived conforming to each region of these phase portraits. We also apply the… More >

  • Open Access

    ARTICLE

    Novel Analysis of Two Kinds Hybrid Models in Ferro Martial Inserting Variable Lorentz Force Past a Heated Disk: An Implementation of Finite Element Method

    Enran Hou, Umar Nazir, Samaira Naz, Muhammad Sohail, Muhammad Nadeem, Jung Rye Lee, Choonkil Park, Ahmed M. Galal
    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.2, pp. 1393-1411, 2023, DOI:10.32604/cmes.2022.022500
    (This article belongs to this Special Issue: Fractal-Fractional Models for Engineering & Sciences)
    Abstract In this article, the rheology of Ferro-fluid over an axisymmetric heated disc with a variable magnetic field by considering the dispersion of hybrid nanoparticles is considered. The flow is assumed to be produced by the stretching of a rotating heated disc. The contribution of variable thermophysical properties is taken to explore the momentum, mass and thermal transportation. The concept of boundary layer mechanism is engaged to reduce the complex problem into a simpler one in the form of coupled partial differential equations system. The complex coupled PDEs are converted into highly nonlinear coupled ordinary differential equations system (ODEs) and the… More >

  • Open Access

    ARTICLE

    Numerical Simulation of the Fractional-Order Lorenz Chaotic Systems with Caputo Fractional Derivative

    Dandan Dai, Xiaoyu Li, Zhiyuan Li, Wei Zhang, Yulan Wang
    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.2, pp. 1371-1392, 2023, DOI:10.32604/cmes.2022.022323
    (This article belongs to this Special Issue: Fractal-Fractional Models for Engineering & Sciences)
    Abstract Although some numerical methods of the fractional-order chaotic systems have been announced, high-precision numerical methods have always been the direction that researchers strive to pursue. Based on this problem, this paper introduces a high-precision numerical approach. Some complex dynamic behavior of fractional-order Lorenz chaotic systems are shown by using the present method. We observe some novel dynamic behavior in numerical experiments which are unlike any that have been previously discovered in numerical experiments or theoretical studies. We investigate the influence of , , on the numerical solution of fractional-order Lorenz chaotic systems. The simulation results of integer order are in… More >

  • Open Access

    ARTICLE

    Cushioning Performance of Hilbert Fractal Sandwich Packaging Structures under Quasi-Static Compressions

    Xingye Xu, Haiyan Song, Lijun Wang
    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.1, pp. 275-292, 2023, DOI:10.32604/cmes.2022.022637
    (This article belongs to this Special Issue: Fractal-Fractional Models for Engineering & Sciences)
    Abstract The sandwich structure of cushioning packaging has an important influence on the cushioning performance. Mathematical fractal theory is an important graphic expression. Based on Hilbert fractal theory, a new sandwich structure was designed. The generation mechanism and recurrence formula of the Hilbert fractal were expressed by Lin’s language, and the second-order Hilbert sandwich structure was constructed from thermoplastic polyurethane. The constitutive model of the hyperelastic body was established by using the finite element method. With the unit mass energy absorption as the optimization goal, the fractal sandwich structure was optimized, and the best result was obtained when the order was… More >

  • Open Access

    ARTICLE

    The Fractional Investigation of Fornberg-Whitham Equation Using an Efficient Technique

    Hassan Khan, Poom Kumam, Asif Nawaz, Qasim Khan, Shahbaz Khan
    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.1, pp. 259-273, 2023, DOI:10.32604/cmes.2022.021332
    (This article belongs to this Special Issue: Fractal-Fractional Models for Engineering & Sciences)
    Abstract In the last few decades, it has become increasingly clear that fractional calculus always plays a very significant role in various branches of applied sciences. For this reason, fractional partial differential equations (FPDEs) are of more importance to model the different physical processes in nature more accurately. Therefore, the analytical or numerical solutions to these problems are taken into serious consideration and several techniques or algorithms have been developed for their solution. In the current work, the idea of fractional calculus has been used, and fractional Fornberg Whitham equation (FFWE) is represented in its fractional view analysis. A well-known method… More >

Share Link

WeChat scan