2024 January - 73 articles
This paper focuses on the analysis of a coupled system governed by a Caputo-fractional derivative with q-integral-coupled boundary conditions. This system is particularly relevant in modeling multi-atomic systems, including scenarios involving adsorb...
This article presents a few fixed-point results under Matkowski-type functional contractive mapping using locally
Recently, a number of researchers from different fields have taken a keen interest in the domain of fractional q-calculus on the basis of fractional integrals and derivative operators. This has been used in various scientific research and technology...
We explore the existence, uniqueness, and multiplicity of positive solutions to a system of fractional q-difference equations that include fractional q-integrals. This investigation is carried out under coupled multi-point boundary conditions featuri...
This paper deepens some results on a Mandelbrot set and Julia sets of Caputo’s fractional order. It is shown analytically and computationally that the classical Mandelbrot set of integer order is a particular case of Julia sets of Caputo-like f...
The current study discusses a novel approach for numerically solving MTVO-TFDWEs under various conditions, such as IBCs and DBCs. It uses a class of GSJPs that satisfy the given conditions (IBCs or DBCs). One of the important parts of our method is e...
The objective of this article is to introduce the
Numerous studies have observed and analyzed the dynamics of language change from a diffusion perspective. As a complex and changeable system, the process of language change is characterized by a long memory that conforms to ultraslow diffusion. Howev...
In this article, a considerably efficient predictor-corrector method (PCM) for solving Atangana–Baleanu Caputo (ABC) fractional differential equations (FDEs) is introduced. First, we propose a conventional PCM whose computational speed scales w...
Detrital zircon geochronology plays a crucial role in provenance analysis, serving as one of the fundamental strategies. The age spectrum of detrital zircons collected from the sedimentary unit of interest is often compared or correlated with that of...
In this paper, we derive an explicit formula of solutions to Hilfer linear fractional integro-differential equations with a variable coefficient in a weighted space, and obtain the existence and uniqueness of solutions for fractional kinetic equation...
The purpose of this study is to explore the existence and uniqueness of the best proximity points for
This study presents the tilt integral derivative (TID) controller technique for controlling the speed of BLDC motors in order to improve the real-time control of brushless direct current motors in electric vehicles. The TID controller is applied to t...
This paper presents a new approach to analyzing the components of centrifuge rotor vibrograms using a 2D trajectory fractal analysis based on the Detrended Moving Average method. The method identifies the different noise oscillatory behavior of the r...
The theory and applications of differential equations have played an essential role both in the development of mathematics and in exploring new horizons in the applied sciences [...]
This manuscript focuses on new generalizations of q-Mittag-Leffler functions, called generalized hyper q-Mittag-Leffler functions, and discusses their regions of convergence and various fractional q operators. Moreover, the solutions to the q-fractio...
In order to describe neuronal dynamics on different time-scales, we propose a stochastic model based on two coupled fractional stochastic differential equations, with different fractional orders. For the specified choice of involved functions and par...
Fractal dimension, as a common nonlinear dynamics metric, is extensively applied in biomedicine, fault diagnosis, underwater acoustics, etc. However, traditional fractal dimension can only analyze the complexity of the time series given a single chan...
Remaining useful life prediction guarantees a reliable and safe operation of turbofan engines. Long-range dependence (LRD) and heavy-tailed characteristics of degradation modeling make this method advantageous for the prediction of RUL. In this study...
This paper proposes an active disturbance rejection control (ADRC) architecture for a permanent magnet synchronous motor (PMSM) position servo system. The presented method achieved enhanced tracking and disturbance rejection performance with a limite...
In this paper, we use the finite volume element method (FVEM) to approximate a one-dimensional, time fractional generalized Burgers’ equation. We construct the fully discrete finite volume element scheme for this equation by approximating the t...
In this paper, we investigate the controllability conditions of linear control systems involving distinct local fractional derivatives. Sufficient conditions for controllability using Kalman rank conditions and the Gramian matrix are presented. We sh...
In this work, a fully discrete mixed finite element (MFE) scheme is designed to solve the multi-term time-fractional reaction–diffusion equations with variable coefficients by using the well-known
The fractal dimension (D) is a very useful indicator for recognizing images. The fractal dimension increases as the pattern of an image becomes rougher. Therefore, images are frequently described as certain models of fractal geometry. Among the model...
The quantification of the irregular morphology and distribution pattern of mineral grains is an essential but challenging task in ore-related mineralogical research, allowing for tracing the footprints of pattern-forming geological processes that are...
Deep low-rank coalbed methane (CBM) resources are numerous and widely distributed in China, although their exploration remains in its infancy. In this work, gas adsorption (N2/CO2), mercury intrusion porosimetry, and 3D CT reconstruction were perform...
This article aims to use various fixed-point techniques to study the stability issue of the impulsive Volterra integral equation in the sense of Ulam–Hyers (sometimes known as Hyers–Ulam) and Hyers–Ulam–Rassias. By eliminating...
This article investigates the differential privacy of the initial state for nabla discrete fractional-order dynamic systems. A novel differentially private Gaussian mechanism is developed which enhances the system’s security by injecting random...
Exploration of mineral resources in the deep sea has become an international trend. However, deep-sea mineral exploration faces challenges such as complex offshore drilling and the weak and mixed signals of ore deposits. Therefore, studying methods f...
Controllability is a fundamental issue in the field of fractional complex network control, yet it has not received adequate attention in the past. This paper is dedicated to exploring the controllability of complex networks involving the Caputo fract...
In this paper, the Caputo-based fractional derivative optimal control model is looked at to learn more about how the human respiratory syncytial virus (RSV) spreads. Model solution properties such as boundedness and non-negativity are checked and fou...
With the gradual depletion of natural sand due to over-exploitation, alternative building materials, such as manufactured sand aggregate (MSA), have attracted much attention. In order to interpret the evolution of pore structure and fractal character...
This study presents multistability mechanisms that can enhance the energy harvesting performance of a piezoelectric energy harvester (PEH) with geometrical nonlinearities. To configure triple potential wells, static bifurcation diagrams in the struct...
This study introduces two innovative methods, the new transform iteration method and the residual power series transform method, to solve fractional nonlinear system Korteweg–de Vries (KdV) equations. These equations, fundamental in describing...
The temporal evolution of the global mean sea level (GMSL) is investigated in the present analysis using the monthly mean values obtained from two sources: a reconstructed dataset and a satellite altimeter dataset. To this end, we use two well-known...
The fractional-order LCL filter, composed of two fractional-order inductors and one fractional-order capacitor, is a novel fractional-order π-type circuit introduced in recent years. Based on mathematical modeling, this article comprehensively stu...
Fractional calculus extends traditional, integer-based calculus to include non-integer orders, offering a powerful tool for a range of engineering applications, including image processing. This work delves into the utility of fractional calculus in t...
Avanish Bhadauria from the Council of Scientific and Industrial Research–Central Electronics Engineering Research Institute (CSIR–CEERI), India, was not included as an author in the original publication [...]
Why do fractals appear in so many domains of science? What is the physical principle that generates them? While it is true that fractals naturally appear in many physical systems, it has so far been impossible to derive them from first physical princ...
In this paper, we introduce the notion of orthogonal
In addressing the issue of strength degradation in saline soil foundations under the salt-freeze coupling effects, a binary medium constitutive model suitable for un-solidified and solidified frozen saline soil is proposed considering both bonding an...
This study explores the connection between the fractal dimensions of time series representing sentiments regarding economic news and the fractal dimensions of correlation networks among companies listed in the Borsa Istanbul star section. While there...
This article describes a low-voltage, low-power fractional-order low-pass filter (FO-LPF) of order 1 + α, which is implemented using a voltage differencing differential difference amplifier (VDDDA). The VDDDA structure is implemented using the...
In this article, we are concerned with a very general integral boundary value problem of Riemann–Liouville derivatives. We will study the problem in Banach space. To be more specific, we are interested in proving the existence of a solution to...
The article outlines a creative approach by fusing ideas from fuzzy contractions, graph mappings, and Kannan mappings to create a brand-new notion known as “Kannan-graph-fuzzy contraction”. This combination of concepts makes it possible t...
This paper addresses the theoretical issues in k-valued logic, which are crucial for developing solutions in various fields of science and technology. One of the fundamental issues is a complete description of the closed classes of functions of three...
Fractional calculus is defined by expanded integer order integration and differentiation. In this paper, multiple mathematical models of a nonlinear dual-tank device are precisely formulated by fractional calculus. Using the accurate model, a multiva...
In this paper, we focus on investigating the well-posedness of backward stochastic differential equations with jumps (BSDEJs) driven by irregular coefficients. We establish new results regarding the existence and uniqueness of solutions for a specifi...
In this paper, the inverse cumulative grey time power model with a Caputo fractional derivative is established, and the solution to the whitening equation is given by the Laplace transform. To improve the prediction accuracy of the model, the linear-...
Ferroresonance is characterized by overvoltage and irregular operation in power systems, which can greatly endanger system equipment. Mechanism analysis of the ferroresonance phenomenon depends mainly on model accuracy. Due to the fractional-order ch...
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