-
HERMITE–HADAMARD TYPE INEQUALITIES FOR ℏ-CONVEX FUNCTION VIA FUZZY INTERVAL-VALUED FRACTIONAL q-INTEGRAL Fractals (IF 4.7) Pub Date : 2024-03-05 HAIYANG CHENG, DAFANG ZHAO, MEHMET ZEKI SARIKAYA
Fractional q-calculus is considered to be the fractional analogs of q-calculus. In this paper, the fuzzy interval-valued Riemann–Liouville fractional (RLF) q-integral operator is introduced. Also new fuzzy variants of Hermite–Hadamard (HH) type and HH–Fejér inequalities, involving ℏ-convex fuzzy interval-valued functions (FIVFs), are presented by making use of the RLF q-integral. The results not only
-
RESEARCH ON FRACTAL HEAT FLOW CHARACTERIZATION OF FINGER SEAL CONSIDERING THE HEAT TRANSFER EFFECT OF CONTACT GAPS ON ROUGH SURFACES Fractals (IF 4.7) Pub Date : 2024-02-28 JUNJIE LEI, MEIHONG LIU
Finger seal is a new flexible dynamic sealing technology, and its heat transfer characteristics and seepage characteristics are one of the main research hotspots. In this paper, based on the fractal theory, a fractal model of the total thermal conductance of the finger seal considering the heat transfer effect of the contact gap of the rough surface is established, a fractal model of the effective
-
A FRACTAL-FRACTIONAL TSUNAMI MODEL CONSIDERING NEAR-SHORE FRACTAL BOUNDARY Fractals (IF 4.7) Pub Date : 2024-02-28 YAN WANG, WEIFAN HOU, KHALED GEPREEL, HONGJU LI
Every fluid problem is greatly affected by its boundary conditions, especially the near-shore seabed could produce an irrevocable harm when a tsunami wave is approaching, and a real-life mathematical model could stave off the worst effect. This paper assumes that the unsmooth seabed is a fractal surface, and fractal-fractional governing equations are established according to physical laws in the fractal
-
THREE PROPERTIES OF FRACTAL NETWORKS BASED ON BEDFORD–MCMULLEN CARPET Fractals (IF 4.7) Pub Date : 2024-02-27 JIAN ZHENG, CHENG ZENG, YUMEI XUE, XIAOHAN LI
In this paper, we consider the networks modeled by several self-affine sets based on the Bedford–Mcmullen carpet. We calculate three properties of the networks, including the cumulative degree distribution, the average clustering coefficient and the average path length. We show that such networks have scale-free and small-world effects.
-
THE IMPACT OF GLOBAL DYNAMICS ON THE FRACTALS OF A QUADROTOR UNMANNED AERIAL VEHICLE (QUAV) CHAOTIC SYSTEM Fractals (IF 4.7) Pub Date : 2024-02-27 MUHAMMAD MARWAN, MAOAN HAN, YANFEI DAI, MEILAN CAI
In this paper, we have extended the concept of advanced Julia function for the discovery of new type of trajectories existing inside outer and inner wings. A dynamical system based on four rotors, referred to as quadrotor unmanned aerial vehicle (QUAV), is considered for the first time to seek the generation of extra wings using fractal theory. Moreover, we have used Julia and advanced Julia function
-
DENG ENTROPY AND INFORMATION DIMENSION FOR COVID-19 AND COMMON PNEUMONIA CLASSIFICATION Fractals (IF 4.7) Pub Date : 2024-02-24 PILAR ORTIZ-VILCHIS, MAYRA ANTONIO-CRUZ, MINGLI LEI, ALDO RAMIREZ-ARELLANO
Motivated by previous authors’ work, where Shannon entropy, box covering and information dimension were applied to quantify pulmonary lesions, this paper extends such a contribution in two fashions: (i) Following the approach to quantify pulmonary lesions with Deng entropy and Deng information dimension obtained through box covering method; (ii) exploiting the Shannon and Deng lesion quantification
-
A 3D FRACTAL MODEL COUPLED WITH TRANSPORT AND ACTION MECHANISMS TO PREDICT THE APPARENT PERMEABILITY OF SHALE MATRIX Fractals (IF 4.7) Pub Date : 2024-02-23 SIYUAN WANG, PENG HOU, XIN LIANG, SHANJIE SU, QUANSHENG LIU
The permeability of shale controls gas transport in shale gas reservoirs. The shale has a complex pore structure at the nanoscale and its permeability is affected by multiple transport and action mechanisms. In this study, a 3D fractal model for predicting the apparent gas permeability of shale matrix is presented, accounting for the effects of the transport mechanisms (bulk gas transport and adsorption
-
A STUDY OF FRACTAL DUAL MOMENTUM INVESTMENT STRATEGY UNDER THE CONSTRAINT OF MULTI-FRACTAL CHARACTERISTICS OF STOCK MARKET Fractals (IF 4.7) Pub Date : 2024-02-23 XU WU, PEIYU WANG, CHI YANG, YAN XIAO
Since the discovery of momentum effect, people have started the journey of using the momentum effect to construct momentum strategies. As a result of coupling cross-sectional and time-series momentum strategy, dual momentum strategy (DM strategy) has been widely used in practice and closely followed by academics. To address the shortcoming of the classical DM strategy that has not considered the multi-fractal
-
MULTIFRACTAL CHARACTERIZATION OF THE INHOMOGENEOUS STRAIN EVOLUTION OF THE DEHYDRATED COAL: INSIGHT FROM COAL MICROSTRUCTURE Fractals (IF 4.7) Pub Date : 2024-02-22 JUNJUN FENG, CHUANHUA XU, FENG YU, JUN PENG, QISONG HUANG, PENG JIN
Underground coal mining in China has gradually moved into deeper seams in recent years, which results in a higher ambient temperature in the mining space and significantly affects the mechanical behavior of coal. In this study, dehydrated coal samples were obtained at different temperatures ranging from 30∘ to 70∘, and the mechanical behavior of the dehydrated coal was investigated through compressive
-
NOVEL PERSPECTIVE TO THE FRACTIONAL SCHRÖDINGER EQUATION ARISING IN OPTICAL FIBERS Fractals (IF 4.7) Pub Date : 2024-02-20 KANG-LE WANG
In this paper, the fractional Schrödinger equation is described with beta derivative, which is used to elucidate the dynamic interaction of ultra-short pulses with quantum properties in optical fibers. This work is to study the solitary wave and periodic solutions of the fractional Schrödinger equation by employing three powerful and simple mathematical approaches like fractional Kudryashov method
-
A d-SUMMABLE APPROACH TO DENG INFORMATION DIMENSION OF COMPLEX NETWORKS Fractals (IF 4.7) Pub Date : 2024-02-19 ALDO RAMIREZ-ARELLANO, JUAN BORY-REYES
Several new network information dimension definitions have been proposed in recent decades, expanding the scope of applicability of this seminal tool. This paper proposes a new definition based on Deng entropy and d-summability (a concept from geometric measure theory). We will prove to what extent the new formulation will be useful in the theoretical and applied points of view.
-
A CLUSTERED FRACTAL DISCRETE FRACTURE NETWORK MODEL FOR FRACTURED COAL Fractals (IF 4.7) Pub Date : 2024-02-16 XIN LIANG, PENG HOU, GUANNAN LIU, YI XUE, JIA LIU, FENG GAO, ZHIZHEN ZHANG
The fracture network in fractured coal is the main channel of coal seam gas flow. Not only the geometric topology properties (such as fractal characteristics) of a single fracture but also the connection topology properties (interconnection characteristics between fractures) of the fracture network have an important impact on the fluid flow in fracture networks. In this study, the connection topology
-
A FRACTAL MODIFICATION OF THE PSEUDO-PARABOLIC EQUATION AND ITS GENERALIZED FRACTAL VARIATIONAL PRINCIPLE Fractals (IF 4.7) Pub Date : 2024-02-14 KANG-JIA WANG, SHUAI LI, PENG XU, FENG SHI
In this work, a new fractal pseudo-parabolic equation is derived by means of He’s fractal derivative. The semi-inverse method (SIM) is employed to develop the generalized fractal variational principle (GFVP), which can reveal the energy conservation law in the fractal space and provide some new insights on the study of the variational method.
-
PHYSICS-INFORMED DEEP AI SIMULATION FOR FRACTAL INTEGRO-DIFFERENTIAL EQUATION Fractals (IF 4.7) Pub Date : 2024-01-31 XUEJUAN LI, RUI ZHAO
Fractal integro-differential equations (IDEs) can describe the effect of local microstructure on a complex physical problem, however, the traditional numerical methods are not suitable for solving the new-born models with the fractal integral and fractal derivative. Here we show that deep learning can be used to solve the bottleneck. By the two-scale transformation, the fractal IDE is first approximately
-
MULTIPARENT FRACTAL IMAGE CODING-BASED METHODS FOR SALT-AND-PEPPER NOISE REMOVAL Fractals (IF 4.7) Pub Date : 2024-01-27 WEIJIE LIANG, XIAOYI LI, ZHIHUI TU, JIAN LU
Salt-and-pepper noise consists of outlier pixel values which significantly impair image structure and quality. Multiparent fractal image coding (MFIC) methods substantially exploit image redundancy by utilizing multiple domain blocks to approximate the range block, partially compensating for the information loss caused by noise. Motivated by this, we propose two novel image restoration methods based
-
EXPLORING INSECTS FREE FLIGHT: ENHANCING THE DIPTERAN FLIGHT MODEL TO INCLUDE FRACTAL EFFECTS Fractals (IF 4.7) Pub Date : 2024-01-27 ALEX ELÍAS-ZÚÑIGA, OSCAR MARTÍNEZ-ROMERO, DANIEL OLVERA-TREJO, IMPERIO ANEL PERALES-MARTÍNEZ, LUIS MANUEL PALACIOS-PINEDA
This paper advances fundamental knowledge of how environmental conditions and physical phenomena at different scales can be included in the differential equation that models the flight dynamics of dipteran insects. The insect’s anatomical capability of modifying their mass inertia and flapping-wing damping properties during flight are included by modeling inertia and damping forces with fractal derivatives
-
MEASURING STRUCTURAL CHANGES OF RECURRENCE PATTERNS IN MULTIFRACTAL AND MULTISCALE ASPECTS BY GENERALIZED RECURRENCE LACUNARITY Fractals (IF 4.7) Pub Date : 2024-01-27 XUEGENG MAO, ZEZHOU LIU, JINZHAO LIU, WANRU XIE, PENGJIAN SHANG, ZHIWEI SHAO
Recurrence lacunarity has been recently proposed to detect dynamical state transitions over various temporal scales. In this paper, we combine suggested distribution moments and introduce multifractal recurrence lacunarity to unearth rich information of trajectories in phase space. By considering generalized moments, it provides an enhanced measurement to account for differences of black pixels in
-
FRACTAL STUDY ON THE PERMEABILITY IN CHARGED MICRO-FRACTURED POROUS MEDIA Fractals (IF 4.7) Pub Date : 2024-01-27 WENYAN LIU, YUZENG DUAN, BOQI XIAO, LIANG LUO, MINGQING ZOU, MINGCHAO LIANG
Fractured porous media is of great significance to the exploration and development of unconventional reservoirs. In this paper, a fractal model for permeability through micro-fractured porous media with consideration of the electric double layer (EDL) effect is proposed based on the fractal theory. The present model indicates that the permeability is a function of the electrokinetic parameters and
-
THE MULTI-PARAMETER FRACTAL–FRACTIONAL INEQUALITIES FOR FRACTAL (P,m)-CONVEX FUNCTIONS Fractals (IF 4.7) Pub Date : 2024-01-27 XIAOMAN YUAN, HÜSEYIN BUDAK, TINGSONG DU
Local fractional calculus theory and parameterized method have greatly assisted in the advancement of the field of inequalities. To continue its enrichment, this study investigates the multi-parameter fractal–fractional integral inequalities containing the fractal (P,m)-convex functions. Initially, we formulate the new conception of the fractal (P,m)-convex functions and work on a variety of properties
-
RESEARCH ON THE K-DIMENSION OF THE SUM OF TWO CONTINUOUS FUNCTIONS AND ITS APPLICATION Fractals (IF 4.7) Pub Date : 2024-01-27 Y. X. CAO, N. LIU, Y. S. LIANG
In this paper, we have done some research studies on the fractal dimension of the sum of two continuous functions with different K-dimensions and approximation of s-dimensional fractal functions. We first investigate the K-dimension of the linear combination of fractal function whose K-dimension is s and the function satisfying Lipschitz condition is still s-dimensional. Then, based on the research
-
ON THE ASYMPTOTIC STABILITY OF A NEW FRACTIONAL-ORDER SLIDING MODE CONTROL WITH APPLICATION TO ROBOTIC SYSTEMS Fractals (IF 4.7) Pub Date : 2024-01-27 FATMA ABDELHEDI, RIM JALLOULI KHLIF, AHMED SAID NOURI, NABIL DERBEL
This paper presents an advanced control strategy based on Fractional-Order Sliding Mode Control (FO-SMC), which introduces a robust solution to significantly improve the reliability of robotic manipulator systems and increase its control performance. The proposed FO-SMC strategy includes a two-key term-based Fractional Sliding Function (FSF) that presents the main contribution of this work. Additionally
-
SOLVABILITY AND OPTIMAL CONTROL OF A SYSTEM OF SEMILINEAR NONLOCAL FRACTIONAL EVOLUTION INCLUSIONS WITH PARTIAL CLARKE SUBDIFFERENTIAL Fractals (IF 4.7) Pub Date : 2024-01-24 LU-CHUAN CENG, BOLING CHEN, SHANLI LIAO, VAN THIEN NGUYEN, JEN-CHIH YAO
The purpose of this paper is to deal with a system governed by a system of semilinear nonlocal fractional evolution inclusions with partial Clarke subdifferential and its optimal control. First, we establish an existence theorem of the mild solution for the presented control system by applying the measure of noncompactness, a fixed point theorem of a condensing multivalued map and some properties of
-
ON THE SEMI-DOMAIN SOLITON SOLUTIONS FOR THE FRACTAL (3+1)-DIMENSIONAL GENERALIZED KADOMTSEV–PETVIASHVILI– BOUSSINESQ EQUATION Fractals (IF 4.7) Pub Date : 2024-01-23 KANG-JIA WANG, JING-HUA LIU, FENG SHI
The aim of this study is to explore some semi-domain soliton solutions for the fractal (3+1)-dimensional generalized Kadomtsev–Petviashvili–Boussinesq equation (GKPBe) within He’s fractal derivative. First, the fractal soliton molecules are plumbed by combining the Hirota equation and fractal two-scale transform. Second, the Bernoulli sub-equation function approach together with the fractal two-scale
-
A NOVEL COMPUTATIONAL APPROACH TO THE LOCAL FRACTIONAL (3+1)-DIMENSIONAL MODIFIED ZAKHAROV–KUZNETSOV EQUATION Fractals (IF 4.7) Pub Date : 2024-01-23 KANG-JIA WANG, FENG SHI
The fractional derivatives have been widely applied in many fields and has attracted widespread attention. This paper extracts a new fractional (3+1)-dimensional modified Zakharov–Kuznetsov equation (MZKe) with the local fractional derivative (LFD) for the first time. Two special functions, namely, the LTδ(Ξδ) and LCδ(Ξδ) functions that are derived on the basis of the Mittag-Leffler function (MLF)
-
APPLICATION OF VARIATIONAL PRINCIPLE AND FRACTAL COMPLEX TRANSFORMATION TO (3+1)-DIMENSIONAL FRACTAL POTENTIAL-YTSF EQUATION Fractals (IF 4.7) Pub Date : 2024-01-23 JUNFENG LU
This paper focuses on the numerical investigation of the fractal modification of the (3+1)-dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation. A variational approach based on the two-scale fractal complex transformation and the variational principle is presented for solving this fractal equation. The fractal potential-YTSF equation can be transformed as the original potential-YTSF equation
-
EDGE-WIENER INDEX OF SIERPINSKI FRACTAL NETWORKS Fractals (IF 4.7) Pub Date : 2024-01-23 YIQI YAO, CAIMIN DU, LIFENG XI
The edge-Wiener index, an invariant index representing the summation of the distances between every pair of edges in the graph, has monumental influence on the study of chemistry and materials science. In this paper, drawing inspiration from Gromov’s idea, we use the finite pattern method proposed by Wang et al. [Average geodesic distance of Sierpinski gasket and Sierpinski networks, Fractals 25(5)
-
FRACTAL ORACLE NUMBERS Fractals (IF 4.7) Pub Date : 2024-01-23 JOEL RATSABY
Consider orbits 𝒪(z,κ) of the fractal iterator fκ(z):=z2+κ, κ∈ℂ, that start at initial points z∈K̂κ(m)⊂ℂ̂, where ℂ̂ is the set of all rational complex numbers (their real and imaginary parts are rational) and K̂κ(m) consists of all such z whose complexity does not exceed some complexity parameter value m (the complexity of z is defined as the number of bits that suffice to describe the real and imaginary
-
QUALITATIVE AND STABILITY ANALYSIS WITH LYAPUNOV FUNCTION OF EMOTION PANIC SPREADING MODEL INSIGHT OF FRACTIONAL OPERATOR Fractals (IF 4.7) Pub Date : 2024-01-19 PEILUAN LI, CHANGJIN XU, MUHAMMAD FARMAN, ALI AKGUL, YICHENG PANG
In an emergency, fear can spread among crowds through one-on-one encounters, with negative societal consequences. The purpose of this research is to create a novel theoretical model of fear (panic) spread in the context of epidemiology during an emergency using the fractal fractional operator. For quantitative analysis, the system’s boundedness and positivity are checked. According to the Arzela Ascoli
-
CONSTRUCTION OF A WEIGHTED FRACTAL INTERPOLATION SURFACE BASED ON MATKOWSKI CONTRACTIONS Fractals (IF 4.7) Pub Date : 2024-01-18 QIAN-RUI ZHONG, HONG-YONG WANG
In this paper, we construct a new kind of weighted recursive iteration function system (IFS) and prove the existence of the unique attractor for the kind of IFS based on the Matkowski fixed point theorem. We confirm that the attractor is a bivariate fractal interpolation surface (FIS), which interpolates a given set of data. In addition, we also provide an upper error estimate of such FISs caused by
-
VIBRATION ANALYSIS OF HEAVY WEAPONS IN TRANSIT BY AIRCRAFT IN FRACTAL SPACE CONSIDERING LOCATION DEVIATION Fractals (IF 4.7) Pub Date : 2024-01-18 YONG-GANG KANG, SHUAI-JIA KOU, SI-REN SONG, YU-ZHEN CHANG, AN-YANG WANG, YONG-GANG CHEN
Air transportation constitutes a significant advancement in enhancing transportation efficiency. Nonetheless, when this modality is employed for the transit of large-scale armaments and equipment, the vibrational properties of these items within the aircraft’s cabin, coupled with potential deviations from their designated installation positions, emerge as critical factors that could compromise the
-
QUANTIFYING THE COVID-19 SHOCK IN CRYPTOCURRENCIES Fractals (IF 4.7) Pub Date : 2024-01-18 LEONARDO H. S. FERNANDES, JOSÉ W. L. SILVA, FERNANDO H. A. ARAUJO, AURELIO F. BARIVIERA
This paper sheds light on the changes suffered in cryptocurrencies due to the COVID-19 shock through a nonlinear cross-correlations and similarity perspective. We have collected daily price and volume data for the seven largest cryptocurrencies considering trade volume and market capitalization. For both attributes (price and volume), we calculate their volatility and compute the Multifractal Detrended
-
HYPER-WIENER INDEX ON LEVEL-3 SIERPINSKI GASKET Fractals (IF 4.7) Pub Date : 2024-01-18 JIAJUN XU, LIFENG XI
The hyper-Wiener index plays an important role in chemical graph theory. In this paper, using the technique named finite pattern, we discuss the hyper-Wiener index on level-3 Sierpinski gasket which is a self-similar fractal.
-
MIXED MULTIFRACTAL SPECTRA OF HOMOGENEOUS MORAN MEASURES Fractals (IF 4.7) Pub Date : 2024-01-18 JIHED HATTAB, BILEL SELMI, SAURABH VERMA
There are only two kinds of measures in which the mixed multifractal formalism applies, which are self-similar and self-conformal measures. This paper studies the validity and non-validity of the mixed multifractal formalism of other kinds of measures, called irregular/homogeneous Moran measures.
-
A STUDY OF FRACTIONAL HERMITE–HADAMARD–MERCER INEQUALITIES FOR DIFFERENTIABLE FUNCTIONS Fractals (IF 4.7) Pub Date : 2024-01-18 THANIN SITTHIWIRATTHAM, MIGUEL VIVAS-CORTEZ, MUHAMMAD AAMIR ALI, HÜSEYIN BUDAK, İBRAHIM AVCI
In this work, we prove a parameterized fractional integral identity involving differentiable functions. Then, we use the newly established identity to establish some new parameterized fractional Hermite–Hadamard–Mercer-type inequalities for differentiable function. The main benefit of the newly established inequalities is that these inequalities can be converted into some new Mercer inequalities of
-
NOVEL INVESTIGATION OF FRACTIONAL LONG- AND SHORT-WAVE INTERACTION SYSTEM Fractals (IF 4.7) Pub Date : 2024-01-12 KANG-LE WANG
In ocean engineering, the long- and short-wave interaction system represents a crucial nonlinear evolution equation that elucidates the resonant interaction phenomenon between ocean waves. In this study, we describe the fractional long and short-wave interaction (FLSWI) system employing the M-truncated derivative. Subsequently, we employ the extended fractional tanhχ−cothχ and the fractional cschχ
-
FRACTIONAL DYNAMICS OF CHRONIC LYMPHOCYTIC LEUKEMIA WITH THE EFFECT OF CHEMOIMMUNOTHERAPY TREATMENT Fractals (IF 4.7) Pub Date : 2024-01-12 RASHID JAN, NORMY NORFIZA ABDUL RAZAK, SULTAN ALYOBI, ZARYAB KHAN, KAMYAR HOSSEINI, CHOONKIL PARK, SOHEIL SALAHSHOUR, SIRILUK PAOKANTA
Currently, immunotherapy is seen to be the most effective cancer treatment. This is especially true while treating chronic lymphocytic leukemia (CLL), a slow-growing B-lymphocyte neoplasm that gradually compromises the immune system. Mathematical modeling is acknowledged as a key technique for analyzing theoretical and practical challenges in this field of cancer research and others. We were inspired
-
A MATHEMATICAL MODEL FOR NIPAH VIRUS DISEASE BY USING PIECEWISE FRACTIONAL ORDER CAPUTO DERIVATIVE Fractals (IF 4.7) Pub Date : 2024-01-12 KAMAL SHAH, AZIZ KHAN, BAHAAELDIN ABDALLA, THABET ABDELJAWAD, KHALID ALI KHAN
In the Caputo sense, the goal of this paper is to develop a thorough analysis for the Nipah virus sickness under piecewise equations with fractional order derivative. Here, we take into account a SIRD-type model with classes for susceptible, infected, recovered, and dead individuals. We evaluate the solution’s viability using the notion of fractional order derivative. The fundamental reproduction number
-
A NEW FRACTAL-FRACTIONAL HYBRID MODEL FOR STUDYING CLIMATE CHANGE ON COASTAL ECOSYSTEMS FROM THE MATHEMATICAL POINT OF VIEW Fractals (IF 4.7) Pub Date : 2024-01-12 HASIB KHAN, MUHAMMAD ASLAM, ALTAF HUSSAIN RAJPAR, YU-MING CHU, SINA ETEMAD, SHAHRAM REZAPOUR, HIJAZ AHMAD
Rapid emissions of green-house gases (GHGs) are causing global warming, which is wreaking havoc on the earth’s climate system. As a result, the coastal ecosystems of the world are on the verge of becoming endangered. We develop a fractal-fractional hybrid model to estimate the influence of rapid emissions of GHGs on the coastal ecosystems and climate changes. The fractal-fractional climate change model
-
SUBSETS OF POSITIVE AND FINITE MULTIFRACTAL MEASURES Fractals (IF 4.7) Pub Date : 2024-01-10 NAJMEDDINE ATTIA, BILEL SELMI
Sets of infinite multifractal measures are awkward to work with, and reducing them to sets of positive finite multifractal measures is a very useful simplification. The aim of this paper is to show that the multifractal Hausdorff measures satisfy the “subset of positive and finite measure” property. We apply our main result to prove that the multifractal function dimension is defined as the supremum
-
A ONE-DIMENSIONAL CONTINUOUS FUNCTION WITH UNBOUNDED VARIATION Fractals (IF 4.7) Pub Date : 2024-01-10 DONG YANG, XIA YUAN, KANG ZHANG, SHIWEI WU, CHUNXIA ZHAO
In this paper, we consider a function with only one unbounded variation point and study the box dimension of its graph. We prove that the function is continuous and differentiable on a certain interval. Moreover, we show that the function is of unbounded variation on the domain of definition. Using our techniques, we also estimate the box dimension of the graph of the function.
-
NUMERICAL APPROXIMATION AND ANALYSIS OF EPIDEMIC MODEL WITH CONSTANT PROPORTIONAL CAPUTO OPERATOR Fractals (IF 4.7) Pub Date : 2024-01-10 CHANGJIN XU, MUHAMMAD FARMAN, ZIXIN LIU, YICHENG PANG
The social life, economic issues, and health issues resulting from various diseases will be impacted by the use of the epidemiological model to address the negative effects of drinking in society. The paper aims to investigate a nonlinear drinking epidemic fractional SHTR model in the sense of a Constant Proportional Caputo (CPC) operator. For the CPC operator, a stability study of the fractional order
-
A NOTE ON FRACTAL DIMENSION OF RIEMANN–LIOUVILLE FRACTIONAL INTEGRAL Fractals (IF 4.7) Pub Date : 2024-01-06 SUBHASH CHANDRA, SYED ABBAS, YONGSHUN LIANG
This paper intends to study the analytical properties of the Riemann–Liouville fractional integral and fractal dimensions of its graph on ℝn. We show that the Riemann–Liouville fractional integral preserves some analytical properties such as boundedness, continuity and bounded variation in the Arzelá sense. We also deduce the upper bound of the box dimension and the Hausdorff dimension of the graph
-
A NEW ESTIMATION OF BOX DIMENSION OF RIEMANN–LIOUVILLE FRACTIONAL CALCULUS OF CONTINUOUS FUNCTIONS Fractals (IF 4.7) Pub Date : 2024-01-06 JUN-RU WU, ZHE JI, KAI-CHAO ZHANG
This paper establishes a linear relationship between the order of the Riemann–Liouville fractional calculus and the exponent of the Hölder condition, whether the Hölder condition is global, local, or at a single point. We propose and prove a control inequality between the Hölder derivative (Hf(x,α) as defined in Proposition 12) of a continuous function and the Hölder derivative of the Riemann–Liouville
-
CONSTRUCTION OF MONOTONOUS APPROXIMATION BY FRACTAL INTERPOLATION FUNCTIONS AND FRACTAL DIMENSIONS Fractals (IF 4.7) Pub Date : 2024-01-06 BINYAN YU, YONGSHUN LIANG
In this paper, we research on the dimension preserving monotonous approximation by using fractal interpolation techniques. A constructive result of the approximating sequence of self-affine continuous functions has been given, which can converge to the object continuous function of bounded variation on [0,1] monotonously and unanimously, meanwhile their graphs can be any value of the Hausdorff and
-
FRACTAL SURFACES INVOLVING RAKOTCH CONTRACTION FOR COUNTABLE DATA SETS Fractals (IF 4.7) Pub Date : 2024-01-04 MANUJ VERMA, AMIT PRIYADARSHI
In this paper, we prove the existence of the bivariate fractal interpolation function using the Rakotch contraction theory and iterated function system for a countable data set. We also give the existence of the invariant Borel probability measure supported on the graph of the bivariate fractal interpolation function. In particular, we highlight that our theory encompasses the bivariate fractal interpolation
-
α-FRACTAL FUNCTION WITH VARIABLE PARAMETERS: AN EXPLICIT REPRESENTATION Fractals (IF 4.7) Pub Date : 2024-01-04 T. M. C. PRIYANKA, C. SERPA, A. GOWRISANKAR
In this paper, new results on the α-fractal function with variable parameters are presented. The Weyl–Marchaud variable order fractional derivative of an α-fractal function with variable parameters is examined by imposing certain conditions on the scaling factors. Following the investigation of fractional derivative, the definite integral of the α-fractal function with variable parameters is evaluated
-
A FRACTAL-FRACTIONAL ORDER MODEL TO STUDY MULTIPLE SCLEROSIS: A CHRONIC DISEASE Fractals (IF 4.7) Pub Date : 2024-01-04 KAMAL SHAH, BAHAAELDIN ABDALLA, THABET ABDELJAWAD, MANAR A. ALQUDAH
A mathematical model of progressive disease of the nervous system also called multiple sclerosis (MS) is studied in this paper. The proposed model is investigated under the concept of the fractal-fractional order derivative (FFOD) in the Caputo sense. In addition, the tools of nonlinear functional analysis are applied to prove some qualitative results including the existence theory, stability, and
-
FRACTAL SURFACE RECOVERY AND SELF-HEALING CONTRIBUTED TO SUSTAINABLE SUPERHYDROPHOBICITY: A REVIEW Fractals (IF 4.7) Pub Date : 2023-12-27 YUNFEI PENG, ZHIHANG MA, XIAO WANG, JUNRU LI, XINLIN LI, CHUANWEI ZHANG, TIAN HE, GUOQIANG LI, PENGFEI ZHANG
The concept of superhydrophobicity has been widely used after years of theoretical and experimental exploration. Researchers have obtained materials with excellent surface superhydrophobicity for numerous areas (e.g. textiles, paints, and coatings industries), through different design and synthesis methods using low surface energy components (LSECs) and micro/nanohierarchy composite structures. However
-
AN EFFICIENT APPROACH FOR SOLVING THE FRACTAL, DAMPED CUBIC–QUINTIC DUFFING’S EQUATION Fractals (IF 4.7) Pub Date : 2023-12-22 ALEX ELÍAS-ZÚÑIGA, OSCAR MARTÍNEZ-ROMERO, DANIEL OLVERA TREJO, LUIS MANUEL PALACIOS-PINEDA
The main goal of this work is to focus on using He’s two-scale fractal dimension transform, the Caputo–Fabrizio fractional-order derivative, and the harmonic balance and the homotopy methods are applied for deriving the approximate solution of the fractal, damped cubic–quintic Duffing’s equation when the fractional derivative order of the inertia term is not twice of that of the damping term. Numerical
-
COMPLEXITY-BASED ANALYSIS OF THE CORRELATION OF BRAIN AND HEART ACTIVITY IN YOUNGER AND OLDER SUBJECTS Fractals (IF 4.7) Pub Date : 2023-12-19 NAJMEH PAKNIYAT, GAYATHRI VIVEKANANDHAN, NORAZRYANA MAT DAWI, ONDREJ KREJCAR, ROBERT FRISCHER, HAMIDREZA NAMAZI
Studying the activity of organs during aging is a very important research area. On the other hand, simultaneous analysis of the activities of various organs is important to understand how their activities are correlated. For the first time, this research analyzes the brain-heart correlation in younger and older subjects. We analyzed the sample entropy (SampEn) and approximate entropy (ApEn) of EEG
-
FRACTAL MODEL OF FLOW CURRENT IN MICRO ROUGH CAPILLARY TUBES Fractals (IF 4.7) Pub Date : 2023-12-16 SHANSHAN YANG, QIONG SHENG, MINGCHAO LIANG, MINGQING ZOU
Based on the fractal geometry science and the model of flow friction resistance when fluid flows through rough microcapillaries, the formula of diffusion layer thickness and the spatial charge density distribution of the pipe were derived. The relationship between the amount of space charge and the structural parameters of rough elements, relative roughness, liquid conductivity, pipeline diameter,
-
NEURAL NETWORK METHOD FOR PARAMETER ESTIMATION OF FRACTIONAL DISCRETE-TIME UNIFIED SYSTEMS Fractals (IF 4.7) Pub Date : 2023-12-15 ZHI-QIANG WU, GUO-CHENG WU, WEI ZHU
Data-driven learning of the fractional discrete-time unified system is studied in this paper. A neural network method is suggested in the parameter estimation of fractional discrete-time chaotic systems. An optimization problem is obtained and the famous Adam algorithm is employed to train the neural network’s weights and parameters. The parameter estimation result is compared with that of the stepwise
-
FRACTAL STUDY ON INTERPOROSITY FLOW FUNCTION AND SHAPE FACTOR OF A POWER-LAW FLUID IN ROUGH FRACTURED DUAL MEDIA Fractals (IF 4.7) Pub Date : 2023-12-15 SHANSHAN YANG, RUIKE CUI, MINGQING ZOU, QIONG SHENG, SHUAIYIN CHEN, MENGYING WANG
Many scholars have studied the interporosity flow function (IFF) and shape factor. However, the existing research does not consider the complex microstructure of dual media and the influence of fluid types on interporosity flow. In this paper, the anisotropic IFF and shape factor model of power-law fluid in smooth and rough fracture dual media are established by using the rough capillary bundle model
-
THE TWO-SCALE FRACTAL DIMENSION: A UNIFYING PERSPECTIVE TO METABOLIC LAW Fractals (IF 4.7) Pub Date : 2023-12-14 QURA TUL AIN, JI-HUAN HE, XIAO-LI QIANG, ZHENG KOU
The laws governing life should be as simple as possible; however, theoretical investigations into allometric laws have become increasingly complex, with the long-standing debate over the scaling exponent in allometric laws persisting. This paper re-examines the same biological phenomenon using two different scales. On a macroscopic scale, a cell surface appears smooth, but on a smaller scale, it exhibits
-
A SCALING LAW RELATING THE RATE OF DESTRUCTION OF A SOLID TUMOR AND THE FRACTAL DIMENSION OF ITS BOUNDARY Fractals (IF 4.7) Pub Date : 2023-12-13 ÁLVARO G. LÓPEZ, LORENA R. SANJUÁN
In this paper, we investigate the scaling law relating the size of the boundary of a solid tumor and the rate at which it is lysed by a cell population of non-infiltrating cytotoxic lymphocytes. We do it in the context of enzyme kinetics through geometrical, analytical and numerical arguments. Following the Koch island fractal model, a scale-dependent function that describes the constant rate of the
-
STATISTICAL ANALYSIS BY WAVELET LEADERS REVEALS DIFFERENCES IN MULTI-FRACTAL CHARACTERISTICS OF STOCK PRICE AND RETURN SERIES IN TURKISH HIGH FREQUENCY DATA Fractals (IF 4.7) Pub Date : 2023-12-08 SALIM LAHMIRI, AHMET SENSOY, ERDINC AKYILDIRIM, STELIOS BEKIROS
The price and return time series are two distinct features of any financial asset. Hence, examining the evolution of multiscale characteristics of price and returns sequential data in time domain would be helpful in gaining a better understanding of the dynamical evolution mechanism of the financial asset as a complex system. In fact, this is important to understand their respective dynamics and to
-
FRACTAL MODEL FOR EFFECTIVE THERMAL CONDUCTIVITY OF COMPOSITE MATERIALS EMBEDDED WITH A DAMAGED TREE-LIKE BIFURCATION NETWORK Fractals (IF 4.7) Pub Date : 2023-12-08 MINGXING LIU, JUN GAO, BOQI XIAO, PEILONG WANG, YI LI, HUAN ZHOU, SHAOFU LI, GONGBO LONG, YONG XU
Scientists worldwide have always been interested in the study of networks that resemble trees and porous materials. Therefore, based on fractal theory, this paper systematically studies the heat transfer problem of the damaged tree-like networks under different saturations in multi-medium composite materials and derives their dimensionless thermal conductivity (DTC). The research has shown that the
-
A GENERALIZED FRACTAL-BASED APPROACH FOR STRESS-DEPENDENT PERMEABILITY OF POROUS ROCKS Fractals (IF 4.7) Pub Date : 2023-12-07 TONGJUN MIAO, AIMIN CHEN, XIAOYA YANG, BOMING YU
The pore geometry of porous rocks is fundamental for accurate description of stress dependence of effective permeability, which is an important parameter of mass transfer in porous rocks. An important physical assumption that porous rocks contain numerous elliptical or spherical pores has been shown to be successfully applied to many aspects of hydromechanical coupling properties of porous rocks. To
-
FRACTAL DIMENSIONS OF THE LOGARITHM OF CONTINUOUS FUNCTIONS Fractals (IF 4.7) Pub Date : 2023-12-07 PEIZHI LIU
This paper investigates the variation of fractal dimensions of continuous functions under operations. It is found that the Box dimension of the logarithm of positive continuous functions remains constant, and any nonzero real power of a positive continuous function can keep fractal dimensions variation closed. The study also discusses the fractal dimension of logarithmic function with bases of fractal
-
GEODESIC DISTANCES ON SIERPINSKI-LIKE SPONGES AND THEIR SKELETON NETWORKS Fractals (IF 4.7) Pub Date : 2023-12-07 YING LU, QINGCHENG ZENG, JIAJUN XU, LIFENG XI
In this paper, we investigate the equivalence of connectedness for the Sierpinski-like sponge and skeleton networks, and find out the relation between the geodesic distance on the sponge and renormalized shortest path distance on the skeleton networks. Furthermore, under some assumption on the IFS, we obtain the comparability of the Manhattan distance and the geodesic distance on the sponge.