Fractal and Fractional, Volume 6, Issue 11

In this work, the exact and approximate solution for generalized linear, nonlinear, and coupled systems of fractional singular M-dimensional pseudo-hyperbolic equations are examined by using the multi-dimensional Laplace Adomian decomposition method...

Fractional q-calculus plays an extremely important role in mathematics and physics. In this paper, we aim to investigate the existence of triple-positive solutions for nonlinear singular fractional q-difference equation boundary value problems at res...

Fractal dimension (FD) together with advances in imaging technologies has provided an increasing application of digital images to interpret biological phenomena. In ophthalmology, topography-based images are increasingly used in common practices of c...

We apply two mathematical techniques, specifically, the unified solver approach and the exp$(-\phi (\xi \left)\right)$-expansion method, for constructing many new solitary waves, such as bright, dark, and singular soliton solutions via the fractional Biswas...

Image processing remains an area that has impact on the software industry and is a field that is permanently developing in both IT and industrial contexts. Nowadays, the demand for fast computing times is becoming increasingly difficult to fulfill in...

Under the influence of internal and external factors, a fracture network is easily generated in concrete and rock, which seriously endangers project safety. Fractal theory can be used to describe the formation and development of the fracture network...

Impedance control is an important method in robot–environment interaction. In traditional impedance control, the damping force is regarded as a linear viscoelastic model, which limits the description of the dynamic model of the impedance system...

Singular systems, which can be applied to gauge field theory, condensed matter theory, quantum field theory of anyons, and so on, are important dynamic systems to study. The fractional order model can describe the mechanical and physical behavior of...

In the literature, all investigations dealing with regulator design in the AVR loop observe the AVR system as a single input single output (SISO) system, where the input is the generator reference voltage, while the output is the generator voltage. B...

Deformable image registration is a very important topic in the field of image processing. It is widely used in image fusion and shape analysis. Generally speaking, image registration models can be divided into two categories: smooth registration and...

One of the main tasks in the problems of machine learning and curve fitting is to develop suitable models for given data sets. It requires to generate a function to approximate the data arising from some unknown function. The class of kernel regressi...

The fuzzy-number valued up and down $\lambda$-convex mapping is originally proposed as an intriguing generalization of the convex mappings. The newly suggested mappings are then used to create certain Hermite–Hadamard- and Pachpatte-type integra...

In this paper, the sliding-mode control method was used to control a class of general nonlinear fractional-order systems which covers a wide class of chaotic systems. A novel sliding manifold with an additional nonlinear part which achieved better co...

Self-similar fractals can be generated using subdivision and the subdivision curves/surfaces are actually attractors. Such a connection has been studied between fractals and an extended family of subdivision including stationary and non-stationary sc...

Compression and mercury intrusion porosimetry (MIP) tests were conducted to analyze the effect of municipal solid waste incineration fly ash (MSWIFA) content on the mechanical performance and pore structure of geopolymer mortar. The MSWIFA weight con...

Pore structure is one of the important parameters for evaluating reservoirs, critical in controlling the storage capacity and transportation properties of hydrocarbons. The conventional pore characterization method cannot fully reflect the pore netwo...

Abrasion resistance and cracking resistance are two important properties determining the normal operation and reliability of hydropower projects that are subjected to erosion and abrasive action. In this study, polyvinyl alcohol (abbreviated as PVA)...

In this paper, we investigate the exact and approximate controllability, finite time stability, and $\beta$–Hyers–Ulam–Rassias stability of a fractional order neutral impulsive differential system. The controllability criteria is inc...

We continue the development of the basic theory of generalized derivatives as introduced and give some of their applications. In particular, we formulate necessary conditions for extrema, Rolle’s theorem, the mean value theorem, the fundamental...

We begin by introducing some function spaces $L_c^p\left({\mathbb{R}}^{+}\right),X_c^p\left(J\right)$ made up of integrable functions with exponent or power weights defined on infinite intervals, and then we investigate the properties of Mellin convolution operators mapping on these spaces,...

In this paper, a chaotic circuit based on a memcapacitor and meminductor is constructed, and its dynamic equation is obtained. Then, the mathematical model is obtained by normalization, and the system is decomposed and summed by an Adomian decomposit...

Several identification approaches have recently been employed in human identification systems for forensic purposes to decrease human efforts and to boost the accuracy of identification. Dental identification systems provide automated matching by sea...

The investigation of fluctuations and random processes in complex systems and random environments has been attracting much attention for years [...]

An option is the right to buy or sell a good at a predetermined price in the future. For customers or financial companies, knowing an option’s pricing is crucial. It is well recognized that the Black–Scholes model is an effective tool for...

An oscillating second-grade fluid through a rectangular cross duct is studied. A traditional integer time derivative in the kinematic tensors is substituted by a fractional operator that considers the memory characteristics. To treat the fractional g...

Modern science is one of the most-used commodities globally, and it is especially important in determining the sources of various threats faced by the world [...]

In this work, we consider linear and nonlinear fractional stochastic delay systems driven by the Rosenblatt process. With the aid of the delayed Mittag-Leffler matrix functions and the representation of solutions of these systems, we derive the contr...

Zeolite Y and Ti-containing zeolite Y (1%, 2% and 5% TiO₂) were synthesized by a hydrothermal seed-assisted method. In order to evidence the evolution of morphology, structure, and fractal dimensions during the zeolitization process at certain time i...

Fractals play a vital role in modeling the natural environment. The present aim is to investigate the escape criterion to generate specific fractals such as Julia sets, Mandelbrot sets and Multi-corns via F-iteration using complex functions $h\left(z\right)=z^n+c$...

The outbreak of coronavirus (COVID-19) began in Wuhan, China, and spread all around the globe. For analysis of the said outbreak, mathematical formulations are important techniques that are used for the stability and predictions of infectious disease...

In this paper, we introduce grand weighted Herz–Morrey spaces with a variable exponent and prove the boundedness of fractional integrals on these spaces.

Analytically and numerically, the study examines the stability and local bifurcations of a discrete-time $SIR$ epidemic model. For this model, a number of bifurcations are studied, including the transcritical, flip bifurcations, Neimark–Sacker bi...

This paper considers the basic concepts of q-calculus and the principle of subordination. We define a new subclass of q-starlike functions related to the Salagean q-differential operator. For this class, we investigate initial coefficient estimates,...

Identification and monitoring of existing surface water bodies on the Earth are important in many scientific disciplines and for different industrial uses. This can be performed with the help of high-resolution satellite images that are processed aft...

In this paper, we present a comparison of several important methods to solve fuzzy partial differential equations (PDEs). These methods include the fuzzy reduced differential transform method (RDTM), fuzzy Adomian decomposition method (ADM), fuzzy Ho...

The Wheeler–DeWitt equation for a flat and compact Friedmann–Lemaître–Robertson–Walker cosmology at the pre-inflation epoch is studied in the contexts of the standard and fractional quantum cosmology. Working within the...

In this paper, the synchronization of two fractional-order chaotic systems with uncertainties and external disturbances is considered. A fuzzy logic system is utilized to estimate uncertain nonlinearity, and its estimation accuracy is improved by con...

This study examines the Chen–Lee–Liu dynamical equation, which represents the propagation of optical pulses in optical fibers and plasma. A new extended direct algebraic technique and Nucci’s scheme are used to find new solitary wav...

In this paper, within the scope of the local fractional derivative theory, bidirectional propagation system local fractional equations are researched. Compared with the unidirectional propagation of nonlinear waves in a pipeline, the bidirectional pr...

In the present work, we address a nonlinear boundary value problem that models frictional contact with prescribed normal stress between a deformable body and a foundation. The body is nonlinearly elastic, the constitutive law being a subdifferential...

This article employs the Laplace residual power series approach to study nonlinear systems of time-fractional partial differential equations with time-fractional Caputo derivative. The proposed technique is based on a new fractional expansion of the...

In mathematical analysis, the Hausdorff derivatives or the fractal derivatives play an important role. Fixed-point theorems and metric fixed-point theory have varied applications in establishing a unique common solution to differential equations and...

According to available estimates with WHO, cancers are the sixth leading cause of global human morbidity and mortality. Prostate Cancer is the fifth-ranked most lethal among various cancers, and hence it warrants serious, dedicated research for impro...

A nonlinear fractional differential equation with a Caputo derivative of order $\alpha$ is studied. This problem is discretized by using the L1 scheme on an arbitrary nonuniform mesh. By utilizing the Taylor expansion with integral remainder term, an...

Fractional wave equations with time-dependent coefficients are natural generations of classical wave equations which can be used to characterize propagation of wave in inhomogeneous media with frequency-dependent power-law behavior. This paper discus...

In this article, the authors study the comparison of the generalization differential transform method (DTM) and fuzzy variational iteration method (VIM) applied to determining the approximate analytic solutions of fuzzy fractional KdV, K(2,2) and mKd...

Using the Lebedev–Milin inequalities, bounds on the logarithmic coefficients of an analytic function can be transferred to estimates on coefficients of the function itself and related functions. From this fact, the study of logarithmic-related...

This paper deals with the maximum likelihood estimator for the parameter of first-order autoregressive models driven by the stationary Gaussian noises (Colored noise) together with an input. First, we will find the optimal input that maximizes the Fi...

In this article, the distributed optimization problem is studied for a class of fractional-order nonlinear uncertain multi-agent systems (MASs) with unmeasured states. Each agent is represented through a system with unknown nonlinearities, unmeasurab...

In this paper, the synchronization of fractional-order uncertain delayed neural networks with an event-triggered communication scheme is investigated. By establishing a suitable Lyapunov–Krasovskii functional (LKF) and inequality techniques, su...