Showing papers in "Fractals in 2021"
TL;DR: In this article, some attempts have been devoted to investigating the dynamic features of discrete fractional calculus (DFC) systems with complex dynamics, such as DFCs with complex dynamics.
Abstract: In this paper, some attempts have been devoted to investigating the dynamic features of discrete fractional calculus (DFC). To date, discrete fractional systems with complex dynamics have attracted...
177 citations
TL;DR: In this article, the authors proposed a method to improve the frost resistance of face slab concrete in cold regions in China, which is one of the most important issues in concre...
Abstract: Face slab concrete suffers from serious frost damage in the cold regions in China. How to improve the frost resistance of face slab concrete in cold regions is one of the important issues in concre...
131 citations
TL;DR: The utilization of phosphorus slag (PHS) to replace the fly ash in the construction of hydraulic projects has attracted a growing attention in China as mentioned in this paper, and the influence of PHS fineness an...
Abstract: The utilization of phosphorus slag (PHS) to replace the fly ash in the construction of hydraulic projects has attracted a growing attention in China. In this study, the influence of PHS fineness an...
130 citations
TL;DR: In this paper, the abrasion resistance of concrete is considered to be one of the most important factors determining the reliability of dam concrete in southwestern China, and it is shown that concrete's resilience to concrete abrasions depends on the type of concrete used.
Abstract: Dam concrete suffers from serious abrasion damages in southwestern China, the abrasion resistance of concrete is therefore one of the most important factors determining the reliability even the saf...
107 citations
TL;DR: In this article, a fractal model for capillary flow through a single tortuous capillary with roughened surfaces in fibrous porous media is derived, and determined imbibition height and imbibitions mas...
Abstract: In this paper, a fractal model for capillary flow through a single tortuous capillary with roughened surfaces in fibrous porous media is derived. The determined imbibition height and imbibition mas...
97 citations
TL;DR: In this paper, pull-in instability, as an inherent nonlinear problem in the design of electrostatic nano/microelectromechanical systems (N/MEMs), is discussed.
Abstract: Pull-in instability, as an inherent nonlinear problem, continues to become an increasingly important and interesting topic in the design of electrostatic Nano/Micro-electromechanical systems (N/MEM...
80 citations
TL;DR: A concrete beam is a basic element for many applications in architectural engineering, and its vibration property plays an important role in safety and life-span as discussed by the authors, and previous vibration models were bas...
Abstract: A concrete beam is a basic element for many applications in architectural engineering, and its vibration property plays an important role in safety and life-span. Previous vibration models were bas...
65 citations
TL;DR: In this article, the authors elucidate a simple but effective meth-based fractal model for vibrating an oscillator in a porous medium or along an unsmooth surface.
Abstract: When an oscillator vibrates in a porous medium or along an unsmooth surface, a fractal model can be adopted using the two-scale fractal derivative. This paper elucidates a simple but effective meth...
60 citations
57 citations
TL;DR: In this paper, a newly constructed system of equation for Hepatitis B disease in sense of Atanganaa-Balea is presented, where scaling exponent of a hierarchy of cities used to be regarded as a fractional.
Abstract: The scaling exponent of a hierarchy of cities used to be regarded as a fractional. This paper investigates a newly constructed system of equation for Hepatitis B disease in sense of Atanganaa–Balea...
49 citations
TL;DR: In this article, a fractional Mayer neuro-swarming intelligent solver for the numerical treatment of multi-fractional order doubly singular Lane-Emden (LE) equation using c...
Abstract: This research is related to present a novel fractional Mayer neuro-swarming intelligent solver for the numerical treatment of multi-fractional order doubly singular Lane–Emden (LE) equation using c...
TL;DR: The barrier option has been among the most popular path-dependent options where its payoff depends on whether or not the investor can control the investor's income or loss within a certain range as mentioned in this paper.
Abstract: Since the ability to control the investor’s income or loss within a certain range, barrier option has been among the most popular path-dependent options where its payoff depends on whether or not t...
TL;DR: In this article, the fractal characteristics of crack propagation in hydraulic fracturing and the effect of fractal dimension of induced fractures on the rock breakdown pressure were investigated, and the results showed that fractal dimensions of induced fracture induced by crack propagation can affect the fracture breakdown pressure.
Abstract: This paper mainly investigated the fractal characteristics of crack propagation in hydraulic fracturing and the effect of fractal dimension of induced fractures on the rock breakdown pressure. A se...
TL;DR: Calcium carbonate whisker (CW) can work as a cost-effective and environment friendly micro-fiber in reinforcing cementitious composites Influence of high temperature on micro-structure of CW reinf
Abstract: Calcium carbonate whisker (CW) can work as a cost-effective and environment friendly micro-fiber in reinforcing cementitious composites Influence of high temperature on micro-structure of CW reinf
TL;DR: Under the non-smooth condition, many theories obtained by the assumption on the smooth condition become invalid, so a generalized Burgers-Huxley equation (GBHE) with fractal derivative is introduced.
Abstract: Under the non-smooth condition, many theories obtained by the assumption on the smooth condition become invalid, so a generalized Burgers–Huxley equation (GBHE) with fractal derivative is introduce...
TL;DR: In this article, a systematic study to the generalized KdV-Burgers-Kuramoto equation is presented resorting to symmetry methinks for wave motions in fluid dynamics and engineering issues.
Abstract: Wave motions play an important role in fluid dynamics and engineering issues. In this paper, a systematic study to the generalized KdV–Burgers–Kuramoto equation is presented resort to symmetry meth...
TL;DR: In this article, the fundamental aim is to find the iterative solution for generalized quintic co-occurrence problems with respect to nonlinear phenomena associated with physical phenomena, which is a hot topic in the present era.
Abstract: The study of nonlinear phenomena associated with physical phenomena is a hot topic in the present era. The fundamental aim of this paper is to find the iterative solution for generalized quintic co...
TL;DR: In this paper, the analysis of a noninteger-order model for hepatitis B (HBV) under singular type Caputo fractional-order derivative is presented. And the proposed system for an ap...
Abstract: In our research work, we develop the analysis of a noninteger-order model for hepatitis B (HBV) under singular type Caputo fractional-order derivative. We investigated our proposed system for an ap...
TL;DR: The well-known coupled Boussinesq-Burger equation can be used to describe the flow of the shallow water of the harbor as mentioned in this paper, but when the boundary is nonsmooth, it becomes powerless.
Abstract: The well-known coupled Boussinesq–Burger equation can be used to describe the flow of the shallow water of the harbor. But when the boundary is nonsmooth, it becomes powerless. So, the fractal calc...
TL;DR: In this article, Wang et al. gave a short remark on variational principle for the fractal Telegraph equation, where the emphasis was put on temporal temporal properties of fractals.
Abstract: This paper gives a short remark on variational principle for the fractal Telegraph equation [K. L. Wang, S. W. Yao, Y. P. Liu et al., Fractals 28(4) (2020) 2050058], the emphasis is put on temporal...
TL;DR: In this paper, the morphology of a shallow-water wave is affected by the unsmooth boundary, while its peak is rarely changed, and this phenomenon cannot be explained by a differential model.
Abstract: The morphology of a shallow-water wave is affected by the unsmooth boundary, while its peak is rarely changed. This phenomenon cannot be explained by a differential model. This paper adopts a fract...
TL;DR: A discrete fractional Susceptible-Infected-Treatment-Recovered-Susceptible (SITRS) model for simulating the coronavirus (COVID-19) pandemic is presented, taking into account the possibility that people who have been infected before can lose their temporary immunity and get reinfected.
Abstract: In this paper, a discrete fractional Susceptible-Infected-Treatment-Recovered-Susceptible (SITRS) model for simulating the coronavirus (COVID-19) pandemic is presented. The model is a modification ...
TL;DR: In this article, partial integrals and partial derivatives of bivariate fractal interpolation functions (FIFs) were investigated and it was shown that the mixed Riemann-Liouville fractional integral and diferent derivatives of FIFs can be computed with a mixed REMIN-Liu integral.
Abstract: In this paper, we investigate partial integrals and partial derivatives of bivariate fractal interpolation functions (FIFs). We also prove that the mixed Riemann–Liouville fractional integral and d...
TL;DR: In this article, local fractional reduced differential transform (LFRDTM) and LFLVIM (local fractional Laplace variational iteration methods) were used to obtain approximate solutions for coupled KdT.
Abstract: In this paper, we utilize local fractional reduced differential transform (LFRDTM) and local fractional Laplace variational iteration methods (LFLVIM) to obtain approximate solutions for coupled Kd...
TL;DR: In this article, the sine-Gordon expansion method was applied to (2+1)-dimensional Nizhnik-Novikov-Veselov equation and Caudrey-Dodd-Gibbon-Sawada-Kot...
Abstract: In this research paper, we implement the sine-Gordon expansion method to two governing models which are the (2+1)-dimensional Nizhnik–Novikov–Veselov equation and the Caudrey–Dodd–Gibbon–Sawada–Kot...
TL;DR: In this article, the authors mainly considered the Whitham-broer-kaup equations with unsmooth boundaries, and a new fractal derivative was adopted to construct the fractal model.
Abstract: In this paper, we mainly consider the Whitham–Broer–Kaup equations with unsmooth boundaries, and a new fractal derivative is adopted to construct the fractal model. The variational principles of th...
TL;DR: In this paper, the Burgers-Benjamin-Bona-Mahony (BBM) equation is described using the use of the fractal derivative and the variational principle of the BBM equation is defined.
Abstract: In this paper, the Burgers–Benjamin–Bona–Mahony (Burgers–BBM) equation is described according to the use of the fractal derivative. The variational principle of the fractal Burgers–BBM equation is ...
TL;DR: The well-known generalized Benjamin-Bona-Mahony-Burgers (gBBMB) equation becomes invalid under the non-smooth boundary as mentioned in this paper, which is the case for the first time.
Abstract: The well-known generalized Benjamin–Bona–Mahony–Burgers (gBBMB) equation is widely used in the fluid mechanics, but it becomes invalid under the non-smooth boundary. So this paper, for the first ti...