Fractal and Fractional, Volume 6, Issue 2

In this paper, we study a class of second-order delay fractional differential equations with a variable-order Caputo derivative. This type of equation is an extension to ordinary delay equations which are used in the modeling of several biological sy...

This paper is concerned with the existence of solutions for a fully coupled Riemann–Stieltjes, integro-multipoint, boundary value problem of Caputo-type sequential fractional differential equations. The given system is studied with the aid of t...

This paper proposes new numerical algorithms for calculating the time domain responses of fractional order transfer functions (FOTFs). FOTFs are divided into two categories, explicit fractional order transfer functions (EFOTFs) and implicit fractiona...

Using the concept of fractional derivatives of Riemann–Liouville on time scales, we first introduce right fractional Sobolev spaces and characterize them. Then, we prove the equivalence of some norms in the introduced spaces, and obtain their c...

A soil–rock mixture (SRM) is a type of heterogeneous geomaterial, and the particle distribution of SRM can be described by fractal theory. At present, it is difficult to quantify the fractal dimension of a particle size distribution and underst...

Few papers have been published to date regarding the stability of neural networks described by fractional difference operators. This paper makes a contribution to the topic by presenting a variable-order fractional discrete neural network model and b...

In recent years, special functions such as Bessel functions have been widely used in many areas of mathematics and physics. We are essentially motivated by the recent development; in our present investigation, we make use of certain conic domains and...

In this paper, we introduce and study a new subclass of multivalent functions with respect to symmetric points involving higher order derivatives. In order to unify and extend various well-known results, we have defined the class subordinate to a con...

In the current paper, we obtain the boundedness of a rough p-adic fractional integral operator on p-adic central Morrey spaces. Moreover, we establish the $\lambda$-central bounded mean oscillations estimate for commutators of a rough p-adic fractiona...

In this work, using calculations based on the density functional theory, molecular dynamics, non-equilibrium Green functions method, and Monte Carlo simulation, we study electronic and phonon transport in a device based on quasi-fractal carbon nitrid...

A time-fractional substantial diffusion equation of variable order is investigated, in which the variable-order fractional substantial derivative accommodates the memory effects and the structure change of the surroundings of the physical processes w...

Currently, the MgO expansion agent is widely used to reduce the cracking risk of concrete. The influence of MgO reactivity (50 s and 300 s) and dosage (0, 4 wt.% and 8 wt.%, by weight of binder) on the air void, pore structure, permeability and freez...

Let $L=-\mathsf{\Delta }+V$ be a Schrödinger operator, where the potential V belongs to the reverse Hölder class. By the subordinative formula, we introduce the fractional heat semigroup ${\left\{e^{-t{L}^{\alpha }}\right\}}_{t>0}, 0<\alpha <1$, associa...

A generalized structure that is capable of implementing power-law filters derived from 1st and 2nd-order mother filter functions is presented in this work. This is achieved thanks to the employment of Operational Transconductance Amplifiers (OTAs) as...

The present paper presents a study on a problem with a fractional integro-differentiation operator in the boundary condition for an equation with a partial Riemann-Liouville fractional derivative. The unique solvability of the problem is proved. In t...

High-dimensional fractional equations research is a cutting-edge field with significant practical and theoretical implications in mathematics, physics, biological fluid mechanics, and other fields. Firstly, in this paper, the (4 + 1)-dimensional time...

The present paper is devoted to the existence of solution for the Hybrid differential inclusions of the second type. Here, we present the inclusion problem with two multi-valued maps. In addition, it is considered with nonlocal integral boundary cond...

In this paper, we investigate a fractional $p(·)$-Kirchhoff type problem involving variable exponent logarithmic nonlinearity. With the help of the Nehari manifold approach, the existence and multiplicity of nontrivial weak solutions for the abo...

The aim of this article is to consider a class of neutral Caputo fractional stochastic evolution equations with infinite delay (INFSEEs) driven by fractional Brownian motion (fBm) and Poisson jumps in Hilbert space. First, we establish the local and...

In this paper, we introduce new types of general contractions for self mapping on double controlled quasi-metric type spaces, where we prove the existence and uniqueness of fixed disc and circle for such mappings.

In this paper, the new mathematical correlation of two quantum systems that were initially allowed to interact and then separated is being formulated and analyzed. These correlations are illustrated by many examples and are also connected with fracta...

Our paper is devoted to the issue of the existence and uniqueness of common fixed points for two mappings in complete b-metric spaces by virtue of the new functions F and $\theta$, respectively. Moreover, two specific examples to indicate the validity...

This paper deals with the issue of the multi-switching sliding mode combination synchronization (MSSMCS) of fractional order (FO) chaotic systems with different structures and unknown parameters under double stochastic disturbances (SD) utilizing the...

In this article, unsteady free convective heat transport of copper-water nanofluid within a square-shaped enclosure with the dominance of non-uniform horizontal periodic magnetic effect is investigated numerically. Various nanofluids are also used to...

This paper proposes a new image enhancement algorithm. At first, the paper uses the combination of rough set and particle swarm optimization (PSO) algorithm to distinguish the smooth area, edge and texture area of the image. Then, according to the re...

This paper introduces one unique price motion process with fractional Brownian motion. We introduce the imaginary number into the agent’s subjective probability for the reason of convergence; further, the result similar to Ito Lemma is proved....

In this article, the effects of Newtonian heating along with wall slip condition on temperature is critically examined on unsteady magnetohydrodynamic (MHD) flows of Prabhakar-like non integer Maxwell fluid near an infinitely vertical plate under con...

This paper investigates the problem of reduced-order $H_{\infty }$ filter design for singular fractional-order systems with order $0<\alpha <1$. It provides necessary and sufficient conditions for designs of both reduced-order $H_{\infty }$ filters and zer...

Fractures caused by mining are the main form of water inrush disaster. However, the temporal and spatial development characteristics of fractures of the rock mass due to mining are not clearly understood at present. In this paper, two geometric param...

Concrete wall surfaces are prone to cracking for a long time, which affects the stability of concrete structures and may even lead to collapse accidents. In view of this, it is necessary to recognize and distinguish the concrete cracks. Then, the sta...

In this paper, we establish a generalized fractional integrals identity involving some parameters and differentiable functions. Then, we use the newly established identity and prove different generalized fractional integrals inequalities like midpoin...

Many authors have established various integral and differential formulas involving different special functions in recent years. In continuation, we explore some image formulas associated with the product of Srivastava’s polynomials and extended...

In this paper, we analyzed and found the solution for a suitable nonlinear fractional dynamical system that describes coronavirus (2019-nCoV) using a novel computational method. A compartmental model with four compartments, namely, susceptible, infec...

Nuclear magnetic resonance flow equations, also known as the Bloch system, are said to be at the heart of both magnetic resonance imaging (MRI) and nuclear magnetic resonance (NMR) spectroscopy. The main aim of this research was to solve fractional n...

Inequalities related to derivatives and integrals are generalized and extended via fractional order integral and derivative operators. The present paper aims to define an operator containing Mittag-Leffler function in its kernel that leads to deduce...

Fractals are geometric shapes and patterns that may repeat their geometry at smaller or larger scales. It is well established that fractals can describe shapes and surfaces that cannot be represented by the classical Euclidean geometry. An eclectic s...

The application of the fractional calculus in the mathematical modelling of relaxation processes in complex heterogeneous media has attracted a considerable amount of interest lately. The reason for this is the successful implementation of fractional...

The higher-order delay differential equations are used in the describing of many natural phenomena. This work investigates the asymptotic properties of the class of even-order differential equations with several delays. Our main concern revolves arou...

In the paper, $H_{\infty }$ and robust $H_{\infty }$ control for fractional order systems (FOS) with order $0<\alpha <1$ are studied. Firstly, necessary and sufficient conditions of $H_{\infty }$ control and state feedback controller design are proposed. Then,...

In this paper, a new approach is developed to solve a class of first-order fractional initial value problems. The present class is of practical interest in engineering science. The results are based on the Riemann–Liouville fractional derivativ...

An introductory discussion on a (weakly non-local) gradient generalization of some one-dimensional elastic and viscoelastic models, and their fractional extension is provided. Emphasis is placed on the possible implications of micro- and nano- engine...

The purpose of this study is to prove the existence of fractional integral inclusions that are connected to the Hermite–Hadamard and Hermite–Hadamard–Fejér type inequalities for χ-pre-invex fuzzy-interval-valued functions. Some of the related fractio...

Cancer is a prominent source of mortality and morbidity globally, but little is known about how it develops and spreads. Tumor cells are unable to thrive in high-temperature environments, according to recent research. Hyperthermia is the name for thi...

This manuscript mainly focuses on the exact controllability of Sobolev-type Hilfer fractional neutral delay Volterra-Fredholm integro-differential systems. The principal findings of this discussion are established by using the theories on fractional...

Noise tends to limit the quality of wide field electromagnetic method (WFEM) data and exploration results. The existing WFEM denoising methods lack the signal identification process and are only able to filter or eliminate abnormalities in the time o...

In this article, we develop a numerical method based on the operational matrices of shifted Vieta–Lucas polynomials (VLPs) for solving Caputo fractional-order differential equations (FDEs). We derive a new operational matrix of the fractional-o...

In this paper, we propose a modified fractional diffusive SEAIR epidemic model with a nonlinear incidence rate. A constructed model of fractional partial differential equations (PDEs) is more general than the corresponding model of fractional ordinar...

This paper studies the containment control problem for a class of fractional order nonlinear multiagent systems in the presence of arbitrary switchings, unmeasured states, and quantized input signals by a hysteresis quantizer. Under the framework of...

The strength of the soil–structure interface can be mobilised when subjected to cyclic loading. To capture the cyclic mobilisation of the soil–structure interface, an advanced elastoplastic constitutive model is developed within the frame...

In this theory, the existence of a mild solution for a neutral partial integrodifferential nonlocal system with finite delay is presented and proved using the techniques of the Monch–Krasnosel’skii type of fixed point theorem, a measure o...