Fractal and Fractional, Volume 5, Issue 4

A comprehensive understanding of fractional systems plays a pivotal role in practical applications [...]

In this article, we utilize recent generalized fractional operators to establish some fractional inequalities in Hermite–Hadamard and Minkowski settings. It is obvious that many previously published inequalities can be derived as particular cas...

In this research work, our aim is to use the fast algorithm to solve the Rayleigh–Stokes problem for heated generalized second-grade fluid (RSP-HGSGF) involving Riemann–Liouville time fractional derivative. We suggest the modified implici...

In this paper, we study some important basic properties of Dunkl-bounded variation functions. In particular, we derive a way of approximating Dunkl-bounded variation functions by smooth functions and establish a version of the Gauss–Green Theor...

The purpose of the current investigation is to find the numerical solutions of the novel fractional order pantograph singular system (FOPSS) using the applications of Meyer wavelets as a neural network. The FOPSS is presented using the standard form...

Under a new generalized definition of exact controllability we introduced and with a appropriately constructed time delay term in a special complete space to overcome the delay-induced-difficulty, we establish the sufficient conditions of the exact c...

In this study, a fractal dimension-based method has been developed to compute the visual complexity of the heterogeneity in the built environment. The built environment is a very complex combination, structurally consisting of both natural and artifi...

The distance centric parameter in the theory of networks called by metric dimension plays a vital role in encountering the distance-related problems for the monitoring of the large-scale networks in the various fields of chemistry and computer scienc...

In this manuscript, we study the unified integrals recently defined by Rahman et al. and present some new double generalized weighted type fractional integral inequalities associated with increasing, positive, monotone and measurable function $\mathcal{F}$. Also...

In the present work, we study the COVID-19 infection through a new mathematical model using the Caputo derivative. The model has all the possible interactions that are responsible for the spread of disease in the community. We first formulate the mod...

In this paper, we consider the Prabhakar fractional logistic differential equation. By using appropriate limit relations, we recover some other logistic differential equations, giving representations of each solution in terms of a formal power series...

In this article, a new mixed finite element (MFE) algorithm is presented and developed to find the numerical solution of a two-dimensional nonlinear fourth-order Riemann–Liouville fractional diffusion-wave equation. By introducing two auxiliary...

We explore some new variants of the Julia set by developing the escape criteria for a function $sin\left(z^n\right)+az+c$, where $a,c\in \mathbb{C}$, $n\ge 2$, and z is a complex variable, utilizing four distinct fixed point iterative methods. Furthermore, we examine the imp...

Integral inequalities involving many fractional integral operators are used to solve various fractional differential equations. In the present paper, we will generalize the Hermite–Jensen–Mercer-type inequalities for an h-convex function...

In this paper, we study nonlinear fractional $(p,q)$-difference equations equipped with separated nonlocal boundary conditions. The existence of solutions for the given problem is proven by applying Krasnoselskii’s fixed-point theorem and the Ler...

This paper investigates a class of fractional-order delayed impulsive gene regulatory networks (GRNs). The proposed model is an extension of some existing integer-order GRNs using fractional derivatives of Caputo type. The existence and uniqueness of...

This research paper intends to investigate some qualitative analysis for a nonlinear Langevin integro-fractional differential equation. We investigate the sufficient conditions for the existence and uniqueness of solutions for the proposed problem us...

This paper deals with the study and analysis of several rational approximations to approach the behavior of arbitrary-order differentiators and integrators in the frequency domain. From the Riemann–Liouville, Grünwald–Letnikov and Ca...

A Caputo-type fractional-order mathematical model for “metapopulation cholera transmission” was recently proposed in [Chaos Solitons Fractals 117 (2018), 37–49]. A sensitivity analysis of that model is done here to show the accuracy...

In this paper, we consider the stochastic fractional-space Chiral nonlinear Schrödinger equation (S-FS-CNSE) derived via multiplicative noise. We obtain the exact solutions of the S-FS-CNSE by using the Riccati equation method. The obtained solu...

A fractional calculus concept is considered in the framework of a Volterra type integro-differential equation, which is employed for the self-consistent description of the high-gain free-electron laser (FEL). It is shown that the Fox H-function is th...

This paper studies a fractional-order chaotic system with sine non-linearities and highlights its dynamics using the Lyapunov spectrum, bifurcation analysis, stagnation points, the solution of the system, the impact of the fractional order on the sys...

Experimental data collected to provide us with information on the course of dielectric relaxation phenomena are obtained according to two distinct schemes: one can measure either the time decay of depolarization current or use methods of the broadban...

We first consider the damped wave inequality $\frac{{\partial }^{2}u}{\partial t^2}-\frac{{\partial }^{2}u}{\partial x^2}+\frac{\partial u}{\partial t}\ge x^{\sigma }{\left|u\right|}^p,t>0,x\in (0,L),$ where $L>0$, $\sigma \in \mathbb{R}$, and $p>1$, under the Dirichlet boundary conditions $\left(u\right(t,0),u(t,L\left)\right)=\left(f\right(t),g(t\left)\right),t\&g$...

In this paper, the quasi-projective synchronization of distributed-order recurrent neural networks is investigated. Firstly, based on the definition of the distributed-order derivative and metric space theory, two distributed-order differential inequ...

In this work, by establishing new asymptotic properties of non-oscillatory solutions of the even-order delay differential equation, we obtain new criteria for oscillation. The new criteria provide better results when determining the values of coeffic...

In this study, we propose a novel fractional-order Jerk system. Experiments show that, under some suitable parameters, the fractional-order Jerk system displays a chaotic phenomenon. In order to suppress the chaotic behavior of the fractional-order J...

We consider random time changes in Markov processes with killing potentials. We study how random time changes may be introduced in these Markov processes with killing potential and how these changes may influence their time behavior. As applications,...

The scale dependence of the effective anti-plane shear modulus response in microstructures with statistical ergodicity and spatial wide-sense stationarity is investigated. In particular, Cauchy and Dagum autocorrelation functions which can decouple t...

In this paper, we study the exact asymptotic separation rate of two distinct solutions of Caputo stochastic multi-term differential equations (Caputo SMTDEs). Our goal in this paper is to establish results of the global existence and uniqueness and c...

The present manuscript focuses on the study of surface wave propagation in a rotating coated viscoelastic half-space and its response to external forces comprised of the magnetic field and gravitational forces. A celebrated normal mode analysis proce...

This manuscript investigates an extended boundary value problem for a fractional pantograph differential equation with instantaneous impulses under the Caputo proportional fractional derivative with respect to another function. The solution of the pr...

In this paper, we establish a new version of Hermite-Hadamard-Fejér type inequality for harmonically convex functions in the form of weighted fractional integral. Secondly, an integral identity and some weighted midpoint fractional Hermite-Had...

Integral operators of a fractional order containing the Mittag-Leffler function are important generalizations of classical Riemann–Liouville integrals. The inequalities that are extensively studied for fractional integral operators are the Hada...

The objective of this work is to study some new oscillation criteria for even-order differential equation with neutral term ${\left(r\left(x\right){\left(z^{\left(n-1\right)}\left(x\right)\right)}^{\gamma }\right)}^{\prime }+q\left(x\right)y^{\gamma }\left(\zeta \left(x\right)\right)=0$. By using the Riccati substitution and comparison technique, several new oscil...

Cement-based materials, including cement and concrete, are the most widely used construction materials in the world. In recent years, the investigation and application of fractal theory in cement-based materials have attracted a large amount of atten...

In this paper, a new approach to find exact solutions is carried out for a generalized unsteady magnetohydrodynamic transport of a rate-type fluid near an unbounded upright plate, which is analyzed for ramped-wall temperature and velocity with consta...

We consider fractional-in-space analogues of Burgers equation and Korteweg-de Vries-Burgers equation on bounded domains. Namely, we establish sufficient conditions for finite-time blow-up of solutions to the mentioned equations. The obtained conditio...

This article contributes to clarifying the questions of whether and how fractal geometry, i.e., some of its main properties, are suitable to characterize architectural designs. This is done in reference to complexity-related aesthetic qualities in ar...

In this paper, we define $(p,q)$-cosine and sine sigmoid polynomials. Based on this, the properties of each polynomial, and the structure and assumptions of its roots, can be identified. Properties can also be determined by the changes in p and q.

Convexity is crucial in obtaining many forms of inequalities. As a result, there is a significant link between convexity and integral inequality. Due to the significance of these concepts, the purpose of this study is to introduce a new class of gene...

Fractional-order mathematical modelling of physical phenomena is a hot topic among various researchers due to its many advantages over positive integer mathematical modelling. In this context, the appropriate solutions of such fractional-order physic...

Nowadays, the manufacturing industry is focused on newer modern manufacturing methods, such as single point incremental forming (SPIF). The popularity of the SPIF process in the manufacturing industry is increasing due to its capability for rapid pro...

This paper presents a novel and general analytical approach: the rational sine-Gordon expansion method and its applications to the nonlinear Gardner and (3+1)-dimensional mKdV-ZK equations including a conformable operator. Some trigonometric, periodi...

In this manuscript, a new class of impulsive fractional Caputo neutral stochastic differential equations with variable delay (IFNSDEs, in short) perturbed by fractional Brownain motion (fBm) and Poisson jumps was studied. We utilized the Carath&eacut...

Considering the large number of fractional operators that exist, and since it does not seem that their number will stop increasing soon at the time of writing this paper, it is presented for the first time, as far as the authors know, a simple and co...

The wear problems are vital to the planetary roller screw mechanism (PRSM) as they have a great influence on transmission accuracy, working efficiency, and service life. However, the wear characteristics of the PRSM have been rarely investigated in t...

A new look at the fractional diffusion equation was done. Using the unified fractional derivative, a new formulation was proposed, and the equation was solved for three different order cases: neutral, dominant time, and dominant space. The solutions...

In this study, a parametric intuitionistic fuzzy multi-objective fractional transportation problem (PIF-MOFTP) is proposed. The current PIF-MOFTP has a single-scalar parameter in the objective functions and an intuitionistic fuzzy supply and demand....

In this paper, we study the improved perturbed nonlinear Schrödinger equation with cubic quadratic nonlinearity (IPNLSE-CQN) to describe the propagation properties of nonlinear periodic waves (PW) in fiber optics. We obtain the chirped periodic...