Fractal and Fractional, Volume 6, Issue 3

In this paper, we prove some new Newton’s type inequalities for differentiable convex functions through the well-known Riemann–Liouville fractional integrals. Moreover, we prove some inequalities of Riemann–Liouville fractional Newt...

In this paper, a family of Ostrowski-type iterative schemes with a biparameter was analyzed. We present the dynamic view of the proposed method and study various conjugation properties. The stability of the strange fixed points for special parameter...

In this work, the F-expansion method is used to find exact solutions of the space-time fractional modified Benjamin Bona Mahony equation and the nonlinear time fractional Schrödinger equation with beta derivative. One of the most efficient and s...

Various function theorists have successfully defined and investigated different kinds of analytic functions. The applications of such functions have played significant roles in geometry function theory as a field of complex analysis. In this work, th...

In this article, a generalized midpoint-type Hermite–Hadamard inequality and Pachpatte-type inequality via a new fractional integral operator associated with the Caputo–Fabrizio derivative are presented. Furthermore, a new fractional iden...

Developing mathematical models of fractional order for physical phenomena and constructing numerical solutions for these models are crucial issues in mathematics, physics, and engineering. Higher order temporal fractional evolution problems (EPs) wit...

Fractional-order neuronal models that include memory effects can describe the rich dynamics of the firing of the neurons. This paper studies synchronization problems in a multiple network of Caputo–Fabrizio type fractional order neurons in whic...

Fractional integral operators are useful tools for generalizing classical integral inequalities. Convex functions play very important role in the theory of mathematical inequalities. This paper aims to investigate the Hadamard type inequalities for a...

In this paper, the nonlinear system of local fractional partial differential equations is solved via local fractional Elzaki transform decomposition method. The local fractional Elzaki decomposition transform method combines a local fractional Elzaki...

In this paper, the extended double (2+1)-dimensional sine-Gorden equation is studied. First of all, using the symmetry method, the corresponding vector fields, Lie algebra and infinitesimal generators are derived. Then, from infinitesimal generators,...

To study the influence of the fractal distribution of particle size on the critical state characteristics of calcareous sand, a type of calcareous sand from a certain reef of the South China Sea was used in this study. For comparison, standard quartz...

In this paper, robust $H_{\infty }$ control for fractional-order switched systems (FOSSs) with uncertainty is studied. Firstly, the fractional-order switching law for FOSSs is proposed. Then, $H_{\infty }$ control for FOSSs is proven based on the switching law...

In this study, the model Riccati equation with variable coefficients as functions, as well as a derivative of a fractional variable order (VO) of the Gerasimov-Caputo type, is used to approximate the data for some physical processes with saturation....

The current manuscript describes the dynamics of a fractional mathematical model of serial killing under the Mittag–Leffler kernel. Using the fixed point theory approach, we present a qualitative analysis of the problem and establish a result t...

In this manuscript, we principally probe into a class of fractional-order tri-neuron neural networks incorporating delays. Making use of fixed point theorem, we prove the existence and uniqueness of solution to the fractional-order tri-neuron neural...

We provide a detailed description of a numerical approach that makes use of the shifted Chebyshev polynomials of the sixth kind to approximate the solution of some fractional order differential equations. Specifically, we choose the fractional Fisher...

In this paper, a class of variable-order fractional interval systems (VO-FIS) in which the system matrices are affected by the fractional order is investigated. Firstly, the sufficient conditions for robust stability of a VO-FIS with a unified order...

This work aims to present a study on the stability analysis of linear and nonlinear incommensurate h-nabla fractional-order difference systems. Several theoretical results are inferred with the help of using some theoretical schemes, such as the Z-tr...

In this paper, a fractional model for the transmission dynamics of cholera was developed. In invariant regions of the model, solutions were generated. Disease-free and endemic equilibrium points were obtained. The basic reproduction number was evalua...

We look at the stochastic fractional-space Bogoyavlenskii equation in the Stratonovich sense, which is driven by multiplicative noise. Our aim is to acquire analytical fractional stochastic solutions to this stochastic fractional-space Bogoyavlenskii...

In the present paper, we establish two Erdélyi-type integrals for Saran’s hypergeometric function $F_K$, which has applications in specific branches of applied physics and statistics (see below). We employ methods based on the k-dimensional...

In this paper, we discuss the existence and uniqueness of solutions for boundary value problems for Hilfer generalized proportional fractional differential equations with multi-point boundary conditions. Firstly, we consider the scalar case for which...

The prediction of permeability and the evaluation of tight oil reservoirs are very important to extract tight oil resources. Tight oil reservoirs contain enormous micro/nanopores, in which the fluid flow exhibits micro/nanoscale flow and has a slip l...

In this study, an efficacious method for solving viscoelastic dynamic plates in the time domain is proposed for the first time. The differential operator matrices of different orders of Bernstein polynomials algorithm are adopted to approximate the t...

In an uncertain situation, data may present in continuous form or discrete form. We have various techniques to deal with continuous data in a realistic situation. However, when data are in discrete form, the existing techniques are inadequate to deal...

Pantograph, a device in which an electric current is collected from overhead contact wires, is introduced to increase the speed of trains or trams. The work aims to study the stability properties of the nonlinear fractional order generalized pantogra...

We investigate a class of fractional time-partial differential equations describing the dynamics of the fast action potential process in contractile myocytes. The system is explored in both one and two dimensional cases. Homogeneous and nonhomogeneou...

The boundary value problem (BVP) for the varying coefficient linear Caputo-type fractional differential equation subject to the mixed boundary conditions on the interval $0\le x\le 1$ was considered. First, the BVP was converted into an equivalent diff...

At present, the consensus problem of fractional complex systems has received more attention. However, there is little literature on the consensus problem of fractional-order complex systems under noise disturbance. In this paper, we present a fractio...

The aim of this research work is to derive some appropriate results for extremal solutions to a class of generalized Caputo-type nonlinear fractional differential equations (FDEs) under nonlinear boundary conditions (NBCs). The aforesaid results are...

In this study, coral powder with different contents and levels of fineness were incorporated into cement; then, the pore structure of a coral powder–cement slurry was measured using the MIP test at days 3 days and 28, respectively. Neimark&rsqu...

Cement-based materials, including cement paste, mortar, and concrete, are the most widely used construction materials in the world [...]

In this paper, we investigate the numerical valuation of European and American options under the time fractional Black-Scholes model. We first apply a coordinate stretching transformation to the asset price so that the spatial region can focus on the...

This paper presents the semi-analytical analysis of the fractional-order non-linear coupled system of Whitham-Broer-Kaup equations. An iterative process is designed to analyze analytical findings to the specified non-linear partial fractional derivat...

Multiple attractors and their fractal basins of attraction can lead to the loss of global stability and integrity of Micro Electro Mechanical Systems (MEMS). In this paper, multistability of a class of electrostatic bilateral capacitive micro-resonat...

This paper investigates the global exponential stability of fractional order complex-valued neural networks with leakage delay and mixed time varying delays. By constructing a proper Lyapunov-functional we established sufficient conditions to ensure...

This paper addresses a new fractional order infectious disease model with saturated incidence and time delay. In the new model, the isolated population and the asymptomatic infected population are considered. The invariant region and positive analysi...

The theme of this study is to present the impacts and importance of the fractional order derivatives of the susceptible, infected and quarantine (SIQ) model based on the coronavirus with the lockdown effects. The purpose of these investigations is to...

This paper proposes to model fractional behaviors using Volterra equations. As fractional differentiation-based models that are commonly used to model such behaviors exhibit several drawbacks and are particular cases of Volterra equations (in the ker...

In this paper, the Fourier spectral method is used to solve the fractional-in-space nonlinear coupled FitzHugh–Nagumo model.Numerical simulation is carried out to elucidate the diffusion behavior of patterns for the fractional 2D and 3D FitzHug...

The topographies of various surfaces have been studied in many fields due to the significant influence that surfaces have on the practical performance of a given sample. A comprehensive evaluation requires the assistance of fractal analysis, which is...

Many recently published research papers examine the representation of nanostructures and biomimetic materials, especially using mathematical methods. For this purpose, it is important that the mathematical method is simple and powerful. Theory of fra...

Contact problems are among the most difficult issues in mathematics and are of crucial practical importance in engineering applications. This paper presents a scaled boundary finite-element method with B-differentiable equations for 3D frictional con...

The purpose of this paper is to investigate a class of initial value problems of fuzzy fractional coupled partial differential equations with Caputo $gH$-type derivatives. Firstly, using Banach fixed point theorem and the mathematical inductive method,...

In this paper, we obtain reverse Minkowski inequalities pertaining to new weighted generalized fractional integral operators. Moreover, we derive several important special cases for suitable choices of functions. In order to demonstrate the efficienc...

The main goal of this study is to demonstrate an existence result of a coupled implicit Riemann-Liouville fractional integral equation. First, we prove a new fixed point theorem in spaces with an extended norm structure. That theorem generalized Darb...

In this paper, we prove a new quantum integral equality involving a parameter, left and right quantum derivatives. Then, we use the newly established equality and prove some new estimates of quantum Ostrowski, quantum midpoint, quantum trapezoidal an...

In many physical models, internal energy will run out without external energy sources. Therefore, finding optimal energy sources and studying their behavior are essential issues. In this article, we study the following variational problem: ${\mathcal{G}}_{ϵ}^{\&l}$...

This paper proposes a numerical method to obtain an approximation solution for the time-fractional Schrödinger Equation (TFSE) based on a combination of the cubic trigonometric B-spline collocation method and the Crank-Nicolson scheme. The fract...

The Hermite-Hadamard inequalities for $\kappa$-Riemann-Liouville fractional integrals (R-LFI) are presented in this study using a relatively novel approach based on Abel-Gontscharoff Green’s function. In this new technique, we first established...