2024 September - 54 articles
Ultrasound imaging is widely used in medical diagnostics due to its non-invasive and real-time capabilities. However, existing methods often overlook the benefits of fractional-order filters for denoising and dehazing. Thus, this work introduces an e...
In this study, a model-free
This paper derives the sharp bounds for Hermite–Hadamard inequalities in the context of Riemann–Liouville fractional integrals. A generalization of Jensen’s inequality called the Jensen–Mercer inequality is used for general po...
The ultrasonic vibration rock-breaking method has been successfully applied to hard rock due to its high efficiency and controllable energy, providing a novel approach for the development of a more efficient, intelligent, safe, and environmentally fr...
Event-triggering mechanisms reported in the existing prescribed-time (PT) control do not adequately capture the dynamic nature of network environments, and are not applied to distributed consensus tracking problems with unknown time delays. Therefore...
In this paper, a novel fractal model for the contact resistance based on axisymmetric sinusoidal asperity is proposed, which focuses on the resistance characteristics of the rough interface at a microscopic scale. By introducing the unique geometric...
We explore the existence, uniqueness, and multiplicity of positive solutions to a system of Hadamard fractional differential equations that contain fractional integral terms. Defined on a finite interval, this system is subject to general coupled non...
This work aims to comprehend the dynamics of neurodegenerative disease using a mathematical model of fractional-order yeast prions. In the context of the Caputo fractional derivative, we here study and examine the solution of this model using the Pre...
In this article, we develop multiplicative fractional versions of Simpson’s and Newton’s formula-type inequalities for differentiable generalized convex functions with the help of established identities. The main motivation for using gene...
The study investigates the nonlinear contagion, tail dependence, and Granger causality relations with TAR-TR-GARCH–copula causality methods for daily Bitcoin, Fintech, energy consumption, and CO2 emissions in addition to examining these series...
Little research has been carried out in terms of modeling and control of analgesia. However, emerging new technology and recent prototypes paved the way for several ideas on pain modeling for control. Recently, such an idea has been proposed for meas...
This research explores nonlocal problems associated with fractional diffusion equations and degenerate hyperbolic equations featuring singular coefficients in their lower-order terms. The uniqueness of the solution is established using the energy int...
In this article, a diffusion component in an SIR model is introduced, and its impact is analyzed using fractional calculus. We have included the diffusion component in the SIR model. in order to illustrate the variations. Here, we have applied the ge...
This study aims to predict the carbon sequestration capacity of Chinese grasslands to address climate change and achieve carbon neutrality goals. Grassland carbon sequestration is a crucial part of the global carbon cycle. However, its capacity is si...
In this work, some properties of the general convolutional operators of general fractional calculus (GFC), which satisfy analogues of the fundamental theorems of calculus, are described. Two types of general fractional (GF) operators on a finite inte...
In this work, novel Ostrowski-type inequalities for dissimilar function classes and generalized fractional integrals (FITs) are presented. We provide a useful identity for differentiable functions under FITs, which results in special expressions for...
In this study, the optimal q-Homotopy Analysis Method (optimal q-HAM) has been used to investigate fractional Abel differential equations. This article is designed as a case study, where several forms of Abel equations, containing Bernoulli and Ricca...
Reactive power dispatch (RPD) in electric power systems, integrated with renewable energy sources, is gaining popularity among power engineers because of its vital importance in the planning, designing, and operation of advanced power systems. The go...
This paper investigates the problem of observer-based control for a class of nonlinear systems described by the Caputo–Hadamard fractional-order derivative. Given the growing interest in fractional-order systems for their ability to capture com...
We utilize Lyapunov exponents to quantitatively assess the hyperchaos and categorize the limit sets of complex dynamical systems. While there are numerous methods for computing Lyapunov exponents in integer-order systems, these methods are not suitab...
Neural Fractional Differential Equations (Neural FDEs) represent a neural network architecture specifically designed to fit the solution of a fractional differential equation to given data. This architecture combines an analytical component, represen...
In this paper, we consider a logarithmic fractional Schrödinger-Poisson system where the potential is a sign-changing function. When the potential is coercive, we get the existence of infinitely many solutions for the system. When the potential...
Fractional cointegration in time series data has been explored by several authors, but panel data applications have been largely neglected. A previous study of ours discovered that the Chen and Hurvich fractional cointegration test for time series wa...
In this article, we focus on examining the existence, uniqueness, and continuous dependence of solutions on initial data for a specific initial boundary value problem which mainly arises from one-dimensional quasi-static contact problems in nonlinear...
This paper studies synchronization behaviors of two sorts of non-linear fractional-order complex spatio-temporal networks modeled by hyperbolic space-varying PDEs (FCSNHSPDEs), respectively, with time-invariant delays and time-varying delays, includi...
This paper presents an application of a fractional-order system on modeling an industrial process system with large inertia and time delay. The traditional integer-order model of the process system is extended to a fractional-order one in this work....
Due to system complexity, research on fuzzy fractional-order, singular perturbation, multi-agent systems (FOSPMASs) remains limited in control theory. This article focuses on the leader-following consensus of fuzzy FOSPMASs with orders in the range o...
The occurrence of landslide hazards significantly induces changes in slope surface displacement. This study conducts an in-depth analysis of the multifractal characteristics and displacement prediction of highway slope surface displacement sequences....
Middle East Respiratory Syndrome (MERS) is a human coronavirus subtype that poses a significant public health concern due to its ability to spread between individuals. This research aims to develop a fractional-order mathematical model to investigate...
In the field of nonlinear mathematical physics, Ablowitz et al.’s algorithm has recently made significant progress in the inverse scattering transform (IST) of fractional-order nonlinear evolution equations (fNLEEs). However, the solved fNLEEs...
We extend two KdVSKR models to fractional KdVSKR models with the Caputo derivative. The KdVSKR equation in (2+1)-dimension, which is a recent extension of the KdVSKR equation in (1+1)-dimension, can model the soliton resonances in shallow water. Appl...
This article investigates the dynamic behaviors of delayed fractional-order memristive fuzzy cellular neural networks via the Lyapunov method. To address the delay terms of fractional-order systems, a novel lemma is provided to make the solutions of...
Function spaces play a crucial role in the study and application of mathematical inequalities. They provide a structured framework within which inequalities can be formulated, analyzed, and applied. They allow for the extension of inequalities from f...
We show maximal regularity estimates for the damped hyperbolic and strongly damped wave equations with periodic initial conditions in a cylindrical domain. We prove that this property strongly depends on a critical combination on the parameters of th...
We looked at the (3+1)-dimensional fractional Kadomtsev–Petviashvili–Boussinesq (KP-B) equation, which comes up in fluid dynamics, plasma physics, physics, and superfluids, as well as when connecting the optical model and hydrodynamic dom...
Multifractal analysis offers a sophisticated method to examine the complex morphology of neurons, which traditionally have been analyzed using monofractal techniques. This study investigates the multifractal properties of two-dimensional neuron proje...
Our recent analysis of empirical limit order flow data in financial markets reveals a power-law distribution in limit order cancellation times. These times are modeled using a discrete probability mass function derived from the Tsallis q-exponential...
In this manuscript, we survey a numerical algorithm based on the combination of the homotopy perturbation method and the Sadik transform for solving the time-fractional nonlinear modified shallow water waves (called Kawahara equation) within the fram...
In medical imaging, noise can significantly obscure critical details, complicating diagnosis and treatment. Traditional denoising techniques often struggle to maintain a balance between noise reduction and detail preservation. To address this challen...
This research is concerned with the existence and uniqueness of solutions for a coupled system of
In this paper, we defined a new family of meromorphic functions whose analytic characterization was motivated by the definition of the multiplicative derivative. Replacing the ordinary derivative with a multiplicative derivative in the subclass of st...
In this paper, we present novel advancements in the theory of bicomplex hypergeometric functions and their applications. We extend the hypergeometric function to bicomplex parameters, analyse its convergence region, and define its integral and deriva...
In this study, we examine Timoshenko systems with boundary conditions featuring two types of fractional dissipations. By applying semigroup theory, we demonstrate the existence and uniqueness of solutions. Our analysis shows that while the system exh...
This study addresses the problem of fractional-order nonlinear containment control of heterogeneous multi-agent systems within a leader–follower framework, focusing on the impact of False Data Injection (FDI) attacks. By employing adaptive mech...
The fractal theory can effectively describe the complexity and multi-scale of concrete under impact load and provide a scientific basis for evaluating concrete’s impact resistance. Therefore, based on the fractal theory, this study carried out...
The quantitative relationship between material microstructures, such as grain distributions, and the nonlinear strain-hardening behaviors of polycrystalline metals has not yet been completely understood. This study finds that the grain correlation di...
In order to obtain the contact resistance of relay contacts more accurately, a novel contact resistance model for the spherical–planar joint interface is constructed based on the three-dimensional fractal theory. In this model, three-dimensiona...
This study investigates the initial value problem of high-order variable-order
In this article, for the first time by using Caputo-type fractional derivatives, we introduce three new subclasses of bi-univalent functions associated with bounded boundary rotation in an open unit disk to obtain non-sharp estimates of the first two...
This paper discusses impulsive effects on fractional differential equations. Two approaches are taken to obtain our results: either with fixed or changing lower limits in Caputo fractional derivatives. First, we derive an existence result for periodi...
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