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# Fractionation - Science method

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In this paper, we study the existence result of solutions for fuzzy nonlinear fractional differential equations involving Caputo differentiability of an arbitrary order 0 < q < 1. As application, an example is included to show the applicability of our result.

Green solvents show several favorable features to be used as extraction and fractionation solvents, such as their ease of preparation and lower cost, and they can be both non-toxic and biodegradable when prepared with natural compounds. Due to their properties, green solvents' application in biomass fractionation has been extensively studied during...

The viscoelasticity of subsurface media is succinctly represented in the generalized wave equation by a fractional time derivative. This generalized viscoelastic wave equation is characterized by the viscoelastic parameter and the viscoelastic velocity, but these parameters are not well formulated and therefore unfavorable for seismic implementatio...

This paper presents an investigation for steady Casson nanofluid flow behavior between parallel plates in the presence of uniform magnetic field. The governing equations are solved via Semi-analytical method, The Akbari Ganji’s Method (AGM). The validity of this method was verified by comparison with results given by using Runge-Kutta. The analysis...

This study investigated the effect of stirring speed, stirring time, and particle weight fraction on the mechanical properties of magnesium matrix composites (Mg-MMCs) synthesized by the stir casting process. In addition, response surface methodology (RSM) and artificial neural network (ANN) models were used to optimize process parameters and creat...

The creep performance of GFRP structures is concerned in the bridge engineering field because the resin in GFRP components belongs to the polymer material, which affects its promotion and application in the infrastructure engineering sector. This study focused on the E-GFRP lamina. The creep behavior of E-GFRP unidirectional lamina were predicted b...

Keywords ψ-Hilfer and Hilfer fractional derivatives ψ-fractional and fractional calculus fractional inequalities of Ostrowski Opial and Poincaré types Abstract After motivation we give a complete background on needed ψ-Hilfer fractional Calculus. Then we produce ψ-Hilfer fractional left and right Taylor formulae. We give also important ψ-Hilfer fra...

In the present investigation, the solubility of two drugs i.e., phenytoin and raloxifene, was obtained in supercritical CO2 at various temperatures and pressures. The obtained results were shown that the solubility of phenytoin and raloxifene, based on mole fraction, was between 0.68 × 10-6 to 15.70 × 10-6 and 0.79 × 10-5 to 8.09 × 10-5, respective...

In this article, we consider a Covid-19 model for a population involving diabetics as a subclass in the fractal-fractional (FF) sense of derivative. The study includes: existence results, uniqueness, stability and numerical simulations. Existence results are studied with the help of fixed-point theory and applications. The numerical scheme of this...

We extend the celebrate De Giorgi-Nash-Moser theory to a wide class of nonlinear equations driven by nonlocal, possibly degenerate, integro-differential operators, whose model is the fractional p -Laplacian operator on the Heisenberg-Weyl group $$\mathbb {H}^n$$ H n . Among other results, we prove that the weak solutions to such a class of problems...

Paper deals with the theoretical investigations of measurement accuracy of optical aberrations by Talbot wavefront sensor in the presence of random amplitude variations. Theoretical prediction of intensity distribution for gratings of any type based on their spatial spectrum is obtained, and it is shown that grating is fully restored in Talbot plan...

Rotating packed beds (RPBs) achieved notable application progress in high-viscosity processes. Mass transfer modeling for viscous fluids, laying the foundation for application research, was a significant and urgent challenge in RPBs. In our previous works, a disk-distributor RPB (DRPB) for facilitating high-viscosity processes was put forward by re...

The objective of the current article is to incorporate the concepts of convexity and Jensen-Mercer inequality with the Caputo-Fabrizio fractional integral operator. Moreover, we present new midpoint versions of Hermite-Hadamard-Mercer (H-H-M) type inequalities for convex functions and the product of two convex functions on fractional integrals. Als...

This paper deals with the production planning and control problem within unreliable Hybrid Manufacturing-Remanufacturing Systems (HMRSs) evolving in a stochastic and dynamic environment. The customer demand can then be fulfilled by either manufacturing of new units or remanufacturing of returned ones. However, both used materials and returns may co...

In this paper, we combine the fractional 𝜓−hyperholomorphic function theory with the fractional calculus with respect to another function. As amain result, a fractional Borel–Pompeiu type formula related to a fractional 𝜓−Fueter operator with respect to a vector-valued function is proved.

The meta distribution of the signal-to-interference-plus-noise ratio (SINR) provides fine-grained information about each link's performance in a wireless system and the reliability of the whole network. While the UAV-enabled network has been studied extensively, most of the works focus on the spatial average performance, such as coverage probabilit...

Depolymerisation of kraft lignin under hydrothermal conditions was investigated at short residence times (1–12 min) with glycerol being used as a capping agent. The weight average molecular weight (M w) of the products decreased within the first minute of residence time, with the inter-unit ether linkages breaking accordingly. Furthermore, the M w...

This article explored how Grade 9 learners solve the concept of multiplication and division of fractions, misconceptions that arise and the root causes of these misconceptions, at a Soweto school in Gauteng. Eight learners were purposefully selected for an interview from the forty Grade 9 participants who were subjected to a written test. Learners'...

We prove a general criterion which ensures that a fractional Calabi--Yau category of dimension $\leq 2$ admits a unique Serre-invariant stability condition, up to the action of the universal cover of $\text{GL}^+_2(\mathbb{R})$. We apply this result to the Kuznetsov component $\text{Ku}(X)$ of a cubic threefold $X$. In particular, we show that all...

In this paper, we consider the Schrödinger equation involving the fractional (p,p1,⋯,pm)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(p,p_1,\dots ,p_m)$$\end{documen...

The purpose of this paper is to study the existence, uniqueness and lifespan of solutions for a fractional Stokes-Transport system. This problem should be understood as a model for sedimentation in a fluid where the viscosity law is given by a fractional Lapalce operator $(- \Delta)^{\alpha/2}$, with $\alpha = 2$ corresponding to the case of a norm...

The problem of deconfinement phases in strongly correlated systems is discussed. In space-time dimension $d=3+1$, a competition of confinement and Coulomb phases occurs, but in $d=2+1$ the confining phase dominates owing to monopole proliferation, but gapless fermion excitations can change the situation. Combining the Kotliar-Ruckenstein representa...

Integral transform play very important role in solving ordinary, partial as well as fractional differential equations. It is also useful for solving integral equations, integro-differential equations and system of equations. In this paper we use Soham transform for solving Abel's integral equations.

In this paper, the existence and uniqueness of the solutions of Caputo fractional delay differential equations under nonlocal and integral boundary value conditions are studied. By using the Banach contraction principle and the Burton and Kirk fixed-point theorem, some new conclusions about the existence and uniqueness of solutions are obtained. An...

In the literature various notions of nonlocal curvature can be found. Here we propose a notion of nonlocal curvature tensor. This we do by generalizing an appropriate representation of the classical curvature tensor and by exploiting some analogies with certain fractional differential operators.

This paper uses numerical simulation to investigate the effects of diluents on the flame structure and NO generation of H2/CO micromixing flames. The results show that under the same thermal power condition, the diluents reduce the flame temperature and decrease the combustion reaction rate and flame propagation velocity. In addition, the diluents...

We consider the problem of supporting payment transactions in an asynchronous system in which up to $f$ validators are subject to Byzantine failures under the control of an adaptive adversary. It was shown that this problem can be solved without consensus by using byzantine quorum systems (requiring at least $2f+1$ validations per transaction in as...

We report the development of a novel measurement system designed to measure bubble properties in bubble curtains (i.e. planar bubble plumes) in situ alongside acoustical measurements. Our approach is based on electrical, contact-based needle sensors in combination with an optical system. The latter is used for calibration and validation purposes. C...

We use HPQCD’s recent lattice QCD determination of B→K scalar, vector and tensor form factors to determine Standard Model differential branching fractions for B→Kℓ+ℓ−, B→Kℓ1+ℓ2− and B→Kνν¯. These form factors are calculated across the full q2 range of the decay and have smaller uncertainties than previous work, particularly at low q2. For B→Kℓ+ℓ− w...

We study photo-assisted transport for the edge states of a two dimensional electron gas in the fractional quantum Hall regime, pinched by a single quantum point contact. We provide a general expression of the photo-assisted current using a Keldysh-Floquet approach, when the AC drive is applied either directly to the edge states, or when it modulate...

Data-driven control methods are strong tools due to their predictions for controlling the systems with a nonlinear dynamic model. In this paper, the Koopman operator is used to linearize the nonlinear dynamic model. Generating the Koopman operator is the most important part of using the Koopman theory. Dynamic mode decomposition (DMD) is used to ob...

The paper is devoted to a stochastic heat equation with a mixed fractional Brownian noise. We investigate the covariance structure, stationarity, upper bounds and asymptotic behavior of the solution. Based on its discrete-time observations, we construct a strongly consistent estimator for the Hurst index H and prove the asymptotic normality for $H<...

Searches for the exclusive decays of the Higgs boson to an $\omega$ meson and a photon or a $K^{*}$ meson and a photon can probe flavour-conserving and flavour-violating Higgs boson couplings to light quarks, respectively. Searches for these decays, along with the analogous $Z$ boson decay to an $\omega$ meson and a photon, are performed with a $pp...

We consider the homogeneous Dirichlet problem for the integral fractional Laplacian (-Δ)s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(-\Delta )^s$$\end{document}. W...

In the present research, we introduce the notion of convex stochastic processes namely; strongly p-convex stochastic processes. We establish a generalized version of Ostrowski-type integral inequalities for strongly p-convex stochastic processes in the setting of a generalized k-fractional Hilfer–Katugampola derivative by using the Hölder and power...

We present analysis of the light curves (LCs) of 77 hydrogen-poor superluminous supernovae (SLSNe I) discovered during the Zwicky Transient Facility Phase I operation. We find that the majority (67%) of the sample can be fit equally well by both magnetar and ejecta–circumstellar medium (CSM) interaction plus ⁵⁶ Ni decay models. This implies that LC...

Despite coupling fractions being extensively used in the interseismic period, the coexistence of locking and creeping mechanisms and the correlation between the coupling fraction and locking depth remain poorly understood because of the lack of a physical model. To overcome these limitations, in this study, we propose a coupling fraction model for...

This is the first report that deals with the effect of yerba mate (YM) and chlorogenic acid (CGA) consumption on blood total creatine phosphokinase (CPK), lactate and irisin levels after a detraining period. Healthy mice (n = 50) were randomly separated into the following experimental groups: SED = sedentary control; TRAIN = mice submitted to train...

This paper presents a search for a new Z' vector gauge boson with the ATLAS experiment at the Large Hadron Collider using pp collision data collected at $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of 139 fb$^{-1}$. The new gauge boson Z' is predicted by $L_{\mu}-L_{\tau}$ models to address observed phenomena that can not be expla...

The main purpose of the present article is to introduce certain new Saigo fractional integral inequalities and their q-extensions. We also studied some special cases of these inequalities involving Riemann-Liouville and Erdelyi-Kober fractional integral operators.

In this paper, a rational difference equation with positive parameters and non-negative conditions is used to determine the presence and direction of the Neimark–Sacker bifurcation. The neimark–Sacker bifurcation of the system is first studied using the characteristic equation. In addition, we study bifurcation invariant curves from the perspective...

We study existence, uniqueness and boundary blow-up profile for fractional harmonic functions on a bounded smooth domain $\Omega \subset \mathbb R^N$. We deal with harmonic functions associated to uniformly elliptic, fully nonlinear nonlocal operators, including the linear case $$ (-\Delta)^s u = 0 \quad \mbox{in} \ \Omega, $$ where $(-\Delta)^s$ d...

We revisit the possibility that neutrinos undergo nonradiative decay. We investigate the potential to extract information on the neutrino lifetime-to-mass ratio from the diffuse supernova neutrino background. To this aim, we explicitly consider the current uncertainties on the core-collapse supernova rate and the fraction of failed supernovae. We p...

In this paper, we define an operator function as a series of operators corresponding to the Taylor series representing the function of the complex variable. In previous papers, we considered the case when a function has a decomposition in the Laurent series with the infinite principal part and finite regular part. Our central challenge is to improv...

We will study evolution algebras A that are free modules of dimension two over domains. We start by making some general considerations about algebras over domains: They are sandwiched between a certain essential D -submodule and its scalar extension over the field of fractions of the domain. We introduce the notion of quasiperfect algebras and we c...

Research about involuntary celibates, or incels, has often relied on indirect texts such as internet forums and discussions as a source of data for qualitative analysis. Using direct qualitative data from interviews with incels (N = 14), this paper examines their beliefs about negative online behaviors such as shit-posting. From the data, we identi...

Reviewer Certificate MDPI Journal Fractal and Fractional, 23 January 2023

We prove an extension of Szarek's optimal Khinchin inequality (1976) for distributions close to the Rademacher one, when all the weights are uniformly bounded by a $1/\sqrt2$ fraction of their total $\ell_2$-mass. We also show a similar extension of the probabilistic formulation of Ball's cube slicing inequality (1986). These results establish the...

We study the Vladimirov-Taibleson operator, a model example of a pseudo-differential operator acting on real- or complex-valued functions defined on a non-Archimedean local field. We prove analogs of classical inequalities for fractional Laplacian, study the counterpart of the Dirichlet problem including the property of boundary H\"older regularity...

This paper proposes a method to improve the fractional interpolation of reference samples in the Versatile Video Coding (VVC) intra prediction. The proposed method uses additional interpolation filters which use more integer-positioned reference samples for prediction according to the frequency information of the reference samples. In VVC, a 4-tap...

The present study elucidates the mineralogical composition of coarser fractions of
the particulate matter using Fourier Transform Infrared Spectroscopy (FTIR).

This paper concerns the boundary value problem for a fractional differential equation involving a generalized Caputo fractional derivative in b−metric spaces. The used fractional operator is given by the kernel k(t, s) = ψ(t) − ψ(s) and the derivative operator 1 ψ (t) d dt. Some existence results are obtained based on fixed point theorem of α-φ−Gra...

In the present article, we explore the correlation between the sign of a Liouville–Caputotype difference operator and the monotone behavior of the function upon which the difference operator acts. Finally, an example is also provided to demonstrate the application and the validation of the results which we have proved herein.

This study investigates the multistability phenomenon and coexisting attractors in the modified Autonomous Van der Pol-Duffing (MAVPD) system and its fractional-order form. The analytical conditions for existence of periodic solutions in the integer-order system via Hopf bifurcation are discussed. In addition, conditions for approximating the solut...

In this paper we are interested in fractional stochactic differential equations (SDEs) with a soft wall. What do we mean by such a type of equation? It has been established that SDE with reflection can be imagined as equations having a hard wall. Now, by introducing repulsion instead of reflection, one obtains an SDE with a soft wall. In contrast t...

Let $A$ and $B$ be invariant linear operators with respect to a decomposition $\{H_{j}\}_{j\in \mathbb{N}}$ of a Hilbert space $\mathcal{H}$ in subspaces of finite dimension. We give necessary and sufficient conditions for the controllability of the Cauchy problem $$ u_t=Au+Bv,\,\,u(0)=u_0,$$ in terms of the (global) matrix-valued symbols $\sigma_A...

Purpose: This study aimed to compare the dosimetric results of flattening filter-free (FFF) vs. flattened (FF) treatment plans for fractionated stereotactic radiotherapy (fSRT), with the goal to highlight potential advantages of FFF beams. Methods: A group of 18 patients with brain metastases treated with fSRT (30 Gy delivered in 5 fractions) were...

This is a contribution to the idea that some proofs in first-order logic are synthetic. Syntheticity is understood here in its classical geometrical sense. Starting from Jaakko Hintikka’s original idea and Allen Hazen’s insights, this paper develops a method to define the ‘graphical form’ of formulae in monadic and dyadic fraction of first-order lo...

Transformation and many other substitution methods have been used to solve non-linear differential fractional equations. In this present work, the homotopy perturbation method to solve the non-linear differential fractional equation with the help of He's Polynomials is provided as the transformation plays an essential role in solving differential l...

Hypergraphs are a powerful abstraction for modeling high-order relations, which are ubiquitous in many fields. A hypergraph consists of nodes and hyperedges (i.e., subsets of nodes); and there have been a number of attempts to extend the notion of $k$-cores, which proved useful with numerous applications for pairwise graphs, to hypergraphs. However...

Redefining viral load suppression (VLS) using lower cutpoints could impact progress towards the UNAIDS 95-95-95 targets. We assessed impacts of lowering the VLS cutpoint on achieving the 95-95-95 VLS target in the Rakai Community Cohort Study. Population VLS fell from 86% to 84% and 76%, respectively, after lowering VLS cutpoints from <1,000 to <20...

In this paper, we propose a numerical scheme of the predictor–corrector type for solving nonlinear fractional initial value problems; the chosen fractional derivative is called the Atangana–Baleanu derivative defined in Caputo sense (ABC). This proposed method is based on Lagrangian quadratic polynomials to approximate the nonlinearity implied in t...

Citation: Abuasbeh, K.; Shafqat, R.; Alsinai, A.; Awadalla, M. Analysis of Controllability of Fractional Functional Random Integroevolution Equations with Delay. Symmetry 2023, 15, 290. https://doi.org/10.3390/ sym15020290 Academic Editor: Dumitru Baleanu Abstract: Various scholars have lately employed a wide range of strategies to resolve two spec...

Picosecond lasers have a very short pulse duration and a high peak power density. When fractional optical delivery systems are attached to picosecond lasers, they generate an array of concentrated microspots with a high fluence surrounded by areas with a low fluence. This article discusses the histologic characteristics and clinical applications of...

For a fractionally integrated Brownian motion (FIBM) of order α∈(0,1],Xα(t), we investigate the decaying rate of P(τSα>t) as t→+∞, where τSα=inf{t>0:Xα(t)≥S} is the first-passage time (FPT) of Xα(t) through the barrier S>0. Precisely, we study the so-called persistent exponent θ=θ(α) of the FPT tail, such that P(τSα>t)=t−θ+o(1), as t→+∞, and by mea...

For $\nu,\nu_i,\mu_j\in(0,1)$, we analyze the semilinear integro-differential equation on the one-dimensional domain $\Omega=(a,b)$ in the unknown $u=u(x,t)$
\[
\mathbf{D}_{t}^{\nu}(\varrho_{0}u)+\sum_{i=1}^{M}\mathbf{D}_{t}^{\nu_{i}}(\varrho_{i}u)
-\sum_{j=1}^{N}\mathbf{D}_{t}^{\mu_{j}}(\gamma_{j}u)
-\mathcal{L}_{1}u-\mathcal{K}*\mathcal{L}_{2}u+f...

In this study, we developed a fiber-optic sensing system with an eight-probe array for measuring the spatial distributions of air volume (void) fractions in bubbly flows. Initially, we performed calibration experiments in a cylindrical tank by using a fiber-optic sensing system with a single probe to determine the relationship between the time frac...

The load imbalance and communication overhead of parallel computing are crucial bottlenecks for galaxy simulations. A successful way to improve the scalability of astronomical simulations is a Hamiltonian splitting method, which needs to identify such regions integrated with smaller timesteps than the global timestep for integrating the entire gala...

In nano-capillaries of large aspect ratio, the attractive image charge force is strong enough to affect the trajectory of ions passing through capillaries and consequently to diminish the fraction of transmitted beam ions. We calculated the theoretically transmitted fraction, using an approached but CPU-friendly expression of the image charge force...

We report the results of the first search for the decay $B_s^0\rightarrow\pi^0\pi^0$ using $121.4\ \rm fb^{-1}$ of data collected at the $\Upsilon(5\rm S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. We observe no signal and set a 90\% confidence level upper limit of $7.7\times 10^{-6}$ on the $B_s^0\rightarro...

The article considers an implicit finite-difference scheme for the Duffing equation with a derivative of a fractional variable order of the Riemann–Liouville type. The issues of stability and convergence of an implicit finite-difference scheme are considered. Test examples are given to substantiate the theoretical results. Using the Runge rule, the...

We study the abstract problem of rounding fractional bipartite $b$-matchings online. The input to the problem is an unknown fractional bipartite $b$-matching, exposed node-by-node on one side. The objective is to maximize the \emph{rounding ratio} of the output matching $\mathcal{M}$, which is the minimum over all fractional $b$-matchings $\mathbf{...

This paper deals with some existence and uniqueness results for a class of problems systems for nonlinear k$$ k $$‐generalized ψ$$ \psi $$‐Hilfer fractional differential equations with periodic conditions. The arguments are based on Mawhin's coincidence degree theory. Furthermore, an illustration is presented to demonstrate the plausibility of our...