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Fractal and Fractional, Volume 6, Issue 8

August 2022 - 58 articles

Cover Story: This paper enhances chaotic systems using fractional orders, multi-scroll grid, dynamic rotation angles, and translational parameters. The rotated system is successfully utilized as a pseudo-random number generator (PRNG) in an image encryption scheme. For hardware realization, the coordinate rotation digital computer (CORDIC) algorithm is used to implement rotation, and the Grünwald–Letnikov (GL) technique is used for solving the fractional-order system. The proposed hardware architectures are realized on a field-programmable gate array (FPGA) using the Xilinx ISE 14.7 on Artix 7 XC7A100T kit. The achieved throughputs are 821.92 Mbits/s and 520.768 Mbits/s for two- and three-dimensional rotating chaotic systems, respectively. View this paper
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Articles (58)

  • Article
  • Open Access
5 Citations
1,697 Views
9 Pages

In this paper, by considering the notions of the invex set, Fréchet differentiability, invexity and pseudoinvexity for the involved functionals of curvilinear integral type, we establish some relations between the solutions of a class of weak...

  • Article
  • Open Access
18 Citations
1,997 Views
9 Pages

On the Physical Fractional Modulations on Langmuir Plasma Structures

  • H. G. Abdelwahed,
  • E. K. El-Shewy,
  • S. Alghanim and
  • Mahmoud A. E. Abdelrahman

Langmuir waves propagate in fractal complex plasma with fractal characteristics, which may cause some plasma particles to be trapped or causes wave turbulences. This phenomenon appears in the form of fractional order equations. Using an effective uni...

  • Article
  • Open Access
7 Citations
1,982 Views
16 Pages

Stability Analysis on Nabla Discrete Distributed-Order Dynamical System

  • Xiang Wu,
  • Xujun Yang,
  • Qiankun Song and
  • Xiaofeng Chen

This paper addresses the problems of the stability of a nabla discrete distributed-order dynamical system (NDDS). Firstly, based on a proposed generalized definition of discrete integral, some related definitions of nabla discrete distributed-order c...

  • Article
  • Open Access
5 Citations
2,197 Views
12 Pages

In this paper, circuit implementation and anti-synchronization are studied in coupled nonidentical fractional-order chaotic systems where a fractance module is introduced to approximate the fractional derivative. Based on the open-plus-closed-loop co...

  • Article
  • Open Access
13 Citations
2,821 Views
19 Pages

The authors of this paper systematically studied the mechanical properties and durability of concrete prepared with copper slag instead of natural aggregates. An analysis index was used to assess compressive strength, and a statistical method was use...

  • Article
  • Open Access
19 Citations
2,954 Views
19 Pages

Computational Analysis of Local Fractional LWR Model Occurring in a Fractal Vehicular Traffic Flow

  • Ved Prakash Dubey,
  • Devendra Kumar,
  • Hashim M. Alshehri,
  • Sarvesh Dubey and
  • Jagdev Singh

In this paper, we implement computational methods, namely the local fractional natural homotopy analysis method (LFNHAM) and local fractional natural decomposition method (LFNDM), to examine the solution for the local fractional Lighthill–Whith...

  • Article
  • Open Access
18 Citations
2,619 Views
13 Pages

The celebrated Korteweg–de Vries and Kadomtsev–Petviashvili (KP) equations are prototypical examples of integrable evolution equations in one and two spatial dimensions, respectively. The question of constructing integrable evolution equa...

  • Article
  • Open Access
5 Citations
1,777 Views
18 Pages

This manuscript mainly discusses the approximate controllability for certain fractional delay evolution equations in Banach spaces. We introduce a suitable complete space to deal with the disturbance due to the time delay. Compared with many related...

  • Article
  • Open Access
18 Citations
3,336 Views
15 Pages

A Compact Triple-Band UWB Inverted Triangular Antenna with Dual-Notch Band Characteristics Using SSRR Metamaterial Structure for Use in Next-Generation Wireless Systems

  • Arshad Karimbu Vallappil,
  • Bilal A. Khawaja,
  • Mohamad Kamal A. Rahim,
  • Muhammad Naeem Iqbal,
  • Hassan T. Chattha and
  • Mohamad Fakrie bin Mohamad Ali

A compact triple-band operation ultra-wideband (UWB) antenna with dual-notch band characteristics is presented in this paper. By inserting three metamaterial (MTM) square split-ring resonators (MTM-SSRRs) and a triangular slot on the radiating patch,...

  • Article
  • Open Access
20 Citations
2,346 Views
12 Pages

The Fractal Characteristics of Soft Soil under Cyclic Loading Based on SEM

  • Bowen Kong,
  • Chen-Xiang Dai,
  • Haibo Hu,
  • Jianzhong Xia and
  • Shao-Heng He

Cyclic loading always results in great damage to the pore structure and fractal characteristics of soft soil. Scanning electron microscope (SEM) can help collect data to describe the microstructure of soft soil. This paper conducted a series of SEM t...

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Fractal Fract. - ISSN 2504-3110