2022 September - 71 articles
This manuscript focuses on the existence of a mild solution Hilfer fractional neutral integro-differential inclusion with almost sectorial operator. By applying the facts related to fractional calculus, semigroup, and Martelli’s fixed point the...
The present paper aims to demonstrate the combined impact of memory, selling price, and exhibited stock on a retailer’s decision to maximizing the profit. Exhibited stock endorses demand and low selling prices are also helpful for creating dema...
We investigate the Cauchy problem for a nonlinear fractional diffusion equation, which is modified using the time-fractional hyper-Bessel derivative. The source function is a gradient source of Hamilton–Jacobi type. The main objective of our cu...
The ability of the Langevin equation to predict coagulation kernels in the transition regime (ranging from ballistic to diffusive) is not commonly discussed in the literature, and previous numerical works are lacking a theoretical justification. This...
The mapping relationships between the conductivity properties are not only of great importance for understanding the transport phenomenon in porous material, but also benefit the prediction of transport parameters. Therefore, a fractal pore-scale mod...
Numerous fields, including the physical sciences, social sciences, and earth sciences, benefit greatly from the application of fractional calculus (FC). The fractional-order derivative is developed from the integer-order derivative, and in recent yea...
This paper aims to present a general identification procedure for fractional first-order plus dead-time (FFOPDT) models. This identification method is general for processes having S-shaped step responses, where process information is collected from a...
A finite element scheme for solving a two-timescale Hadamard time-fractional equation is discussed. We prove the error estimate without assuming the smoothness of the solution. In order to invert the fractional order, a finite-element Levenberg&ndash...
This study investigates the fractional-order Swift–Hohenberg equations using the natural decomposition method with non-singular kernel derivatives. The fractional derivative in the sense of Caputo–Fabrizio is considered. The Adomian decom...
In this paper, we focus on the existence of Hilfer fractional stochastic differential systems via almost sectorial operators. The main results are obtained by using the concepts and ideas from fractional calculus, multivalued maps, semigroup theory,...
In this paper, the transverse vibration of a fractional viscoelastic beam is studied based on the fractional calculus, and the corresponding scheme of a viscoelastic beam is established by using the mixed finite volume element method. The stability a...
In recent years, we found that some multiscale methods applied to fractional differential problems, are easy and efficient to implement, when we use some fractional refinable functions introduced in the literature. In fact, these functions not only g...
Fractional calculus is useful in studying physical phenomena with memory effects. In this paper, the fractional KMM (FKMM) system with beta-derivative in (2+1)-dimensions was studied for the first time. It can model short-wave propagation in saturate...
Interval analysis distinguishes between different types of order relations. As a result of these order relations, convexity and nonconvexity contribute to different kinds of inequalities. Despite this, convex theory is commonly known to rely on Godun...
Autonomous underwater vehicles (AUVs) have broad applications owing to their ability to undertake long voyages, strong concealment, high level of intelligence and ability to replace humans in dangerous operations. AUV motion control systems can ensur...
In this paper, we analyze the novel type of COVID-19 caused by the Omicron virus under a new operator of fractional order modified by Caputo–Fabrizio. The whole compartment is chosen in the sense of the said operator. For simplicity, the model...
This paper consists of a general consideration of a seismic system as a subsystem of another, larger system, exchanging with it by extensive dynamical quantities in a sequential push mode. It is shown that, unlike an isolated closed system described...
In this paper, we focus on the computation of Caputo-type fractional differential equations. A high-order predictor–corrector method is derived by applying the quadratic interpolation polynomial approximation for the integral function. In order...
The issue of adaptive finite-time cluster synchronization corresponding to neutral-type coupled complex-valued neural networks with mixed delays is examined in this research. A neutral-type coupled complex-valued neural network with mixed delays is m...
The impulsive response of the fractional vibration equation
In this work, the fractional novel analytic method (FNAM) is successfully implemented on some well-known, strongly nonlinear fractional partial differential equations (NFPDEs), and the results show the approach’s efficiency. The main purpose is...
This paper proposes an accurate numerical approach for computing the solution of two-dimensional fractional Volterra integral equations. The operational matrices of fractional integration based on the Hybridization of block-pulse and Taylor polynomia...
The fracture of interfacial crack is the main failure type of jointed rock mass. Therefore, it is very important to study the interfacial fracture of jointed rock mass. For the similarity of jointed rock mass and composites (all are composed by two p...
Following the traditional total variational denoising model in removing medical image noise with blurred image texture details, among other problems, an adaptive medical image fractional-order total variational denoising model with an improved sparro...
The Poisson-stopped sum of the Hurwitz–Lerch zeta distribution is proposed as a model for interarrival times and rainfall depths. Theoretical properties and characterizations are investigated in comparison with other two models implemented to p...
This study is concerned with the dynamic investigation and fixed-time synchronization of a fractional-order financial system with the Caputo derivative. The rich dynamic behaviors of the fractional-order financial system with variations of fractional...
The objective of this manuscript is to establish a link between the concept of inequalities and Center-Radius order functions, which are intriguing due to their properties and widespread use. We introduce the notion of the
We examine a viscous Cahn–Hilliard phase-separation model with memory and where the chemical potential possesses a nonlocal fractional Laplacian operator. The existence of global weak solutions is proven using a Galerkin approximation scheme. A...
Fractal analysis is an effective tool to describe real world phenomena. Water evaporation from the soil surface under extreme climatic conditions, such as drought, causes salt to accumulate in the soil, resulting in soil salinization, which aggravate...
Differential equations, both fractional and ordinary, give key tools in understanding the mechanisms of physical systems and solving various problems of nonlinear phenomena [...]
Finite-time synchronization (FTS) of uncertain fractional-order memristive neural networks (FMNNs) with leakage and discrete delays is studied in this paper, in which the impacts of uncertain parameters as well as external disturbances are considered...
Porous alumina ceramics with different porosities were prepared via atmospheric pressure sintering using a sacrificial template method with alumina powder as the raw material and carbon fiber (CF) and graphite as pore-forming agents. The effects of t...
For the first time, a new dissipation-preserving scheme is proposed and analyzed to solve a Caputo–Riesz time-space-fractional multidimensional nonlinear wave equation with generalized potential. We consider initial conditions and impose homoge...
It is necessary to quantitatively describe or illustrate the characteristics of abnormal stock price fluctuations in order to prevent and control financial risks. This paper studies the fractal structure of China’s stock market by calculating t...
This study inspects the issue of robust reliable sampled data control (SDC) for a class of Takagi-Sugeno (TS) fuzzy CE151 Helicopter systems with time-varying delays and linear fractional uncertainties. Specifically, both the variation range and the...
A Hermite fitted block integrator (HFBI) for numerically solving second-order anisotropic elliptic partial differential equations (PDEs) was developed, analyzed, and implemented in this study. The method was derived through collocation and interpolat...
In this study, new midpoint-type inequalities are given through recently generalized Riemann–Liouville fractional integrals. Foremost, we present an identity for a class of differentiable functions including the proposed fractional integrals. T...
The Caputo–Fabrizio fractional integral operator is one of the important notions of fractional calculus. It is involved in numerous illustrative and practical issues. The main goal of this paper is to investigate weighted fractional integral in...
In this paper, the adaptive finite-time control problem for fractional-order systems with uncertainties and unknown dead-zone fault was studied by combining a fractional-order command filter, radial basis function neural network, and Nussbaum gain fu...
A smooth and discontinuous (SD) oscillator is a typical multi-stable state system with strong nonlinear properties and has been widely used in many fields. The nonlinear dynamic characteristics of the system have not been thoroughly investigated beca...
Fractional-order calculus has become a useful mathematical framework to describe the complex super-diffusive process; however, numerical solutions of the two-sided space-fractional super-diffusive model with variable coefficients are difficult to obt...
This paper presents the FEM modeling and simulation of a thin-film bulk acoustic resonator (FBAR) for a tetrachloroethene (PCE) gas-sensing application. A zinc oxide layer is used as a piezoelectric material; an aluminum layer is used as the electrod...
The objective of this work is to investigate analytical solutions of some models of cancer tumors using the Laplace residual power series method (LRPSM). The proposed method was effective and required simple calculations to find the analytic series s...
A bibliometric analysis of publications on fractal theory and thin films is presented in this article. Bibliographic information is extracted from the Web of Science digital database and the bibliographic mapping undertaken using VOSviewer software....
This paper studies the existence of extremal solutions for a nonlinear boundary value problem of Bagley–Torvik differential equations involving the Caputo–Fabrizio-type fractional differential operator with a non-singular kernel. With the...
We continue the study of a non-self-adjoint fractional three-term Sturm–Liouville boundary value problem (with a potential term) formed by the composition of a left Caputo and left Riemann–Liouville fractional integral under Dirichlet typ...
A fractal realizes the quantitative characterization of complex and disordered mining fracture networks, and it is of great significance to grasp the fractal characteristics of rock movement law to guide mine production. To prevent the water-conducti...
Fractional-order PID control is a landmark in the development of fractional-order control theory. It can improve the control precision and accuracy of systems and achieve more robust control results. As a theorem-proving formal verification method, i...
The occurrence and flow of shale gas are substantially impacted by nanopore structures. The fractal dimension provides a new way to explore the pore structures of shale reservoirs. In this study, eight deep shale samples from Longmaxi Formation to Wu...
A second-order sliding mode control (SOSMC) with a fractional module using adaptive fuzzy controller is developed for an active power filter (APF). A second-order sliding surface using a fractional module which can decrease the discontinuities and ch...
of 2
