ANALYSIS OF THE FLOW OF BRINKMAN-TYPE NANOFLUID USING GENERALIZED FOURIER’S AND FICK’S LAWS

The enhancement of the working ability of the industrial fluid is the need of the present era; nanofluid is an emerging field in science and technology. In this study, the Brinkman-type fluid model is used and is generalized using the Fourier’s and Fick’s laws. The graphene oxide nanoparticles are dispersed in the base fluid water. The fractional partial differential equations are then solved via the Laplace and Fourier transform method. The obtained solutions for velocity, heat transfer, and mass transfer are plotted in graphs. The results show that velocity profile decreases for Brinkman-type fluid parameter and volume fraction of the nanoparticles. The plot for the fractional parameter shows that different plots can be drawn for a fixed time and other physical parameters, which is the memory effect.

Investigation of dynamics of SWCNTs and MWCNTs nanoparticles in blood flow using the Atangana–Baleanu time fractional derivative with ramped temperature

This analysis deals with the mixed free convection flow of nanofluid in the presence of porous space. Human blood is supposed to be a base fluid for which the heat transfer characteristics are performed by using the single- and multi-wall carbon nanotubes. The leading equations of the problem are obtained in dimensionless form by following the appropriate non-dimensional variables. The semi-analytical solution for the temperature and velocity field, the famous Atangana–Baleanu time-fractional derivative and Laplace transform techniques are utilized. The effects of different parameters are studied with interesting physical explanations. The summarized results show that the temperature and velocity profile decreases by varying the value of the fractional parameter. An increasing change in velocity is observed for the Grashof number. Moreover, the solution simulated via fractional model for velocity and temperature profile is more consistent and scalable for any value of the fractional parameter.

An explicit plethora of soliton solutions for a new microtubules transmission lines model: A fractional comparison

This paper introduces a new fractional electrical microtubules transmission lines model in the sense of Atangana–Baleanu and beta derivatives to comprehend nonlinear dynamics of the governing system. This structure possesses one of the most important parts in cellular process biology and fractional parameter incorporates the memory effects in microtubules. Also, microtubules are extremely beneficial in cell motility, signaling and intracellular transport. The new extended direct algebraic method is a compelling and persuasive integrating scheme to extract soliton solutions. The retrieved solutions include dark, bright and singular solitons. This model executes a prominent part in exhibiting the wave transmission in nonlinear systems. The novelty and advantage of the proposed method are portrayed by applying it to this model and its dynamical behavior is depicted by 3D and 2D plots. A comparative study of two fractional derivatives at distinct fractional parameter values and graphics of sensitivity analysis is also carried out in this paper.

Generalized Fractional Bézier Curve with Shape Parameters

The construction of new basis functions for the Bézier or B-spline curve has been one of the most popular themes in recent studies in Computer Aided Geometric Design (CAGD). Implementing the new basis functions with shape parameters provides a different viewpoint on how new types of basis functions can develop complex curves and surfaces beyond restricted formulation. The wide selection of shape parameters allows more control over the shape of the curves and surfaces without altering their control points. However, interpolated parametric curves with higher degrees tend to overshoot in the process of curve fitting, making it difficult to control the optimal length of the curved trajectory. Thus, a new parameter needs to be created to overcome this constraint to produce free-form shapes of curves and surfaces while still preserving the basic properties of the Bézier curve. In this work, a general fractional Bézier curve with shape parameters and a fractional parameter is presented. Furthermore, parametric and geometric continuity between two generalized fractional Bézier curves is discussed in this paper, as well as demonstrating the effect of the fractional parameter of curves and surfaces. However, the conventional parametric and geometric continuity can only be applied to connect curves at the endpoints. Hence, a new type of continuity called fractional continuity is proposed to overcome this limitation. Thus, with the curve flexibility and adjustability provided by the generalized fractional Bézier curve, the construction of complex engineering curves and surfaces will be more efficient.

Positron nonextensivity effect on the propagation of dust ion acoustic Gardner waves

Propagation of dust ion-acoustic (DIA) Gardner wave in a dusty electron–positron–ion (e–p–i) plasma is investigated. This plasma consists of q-distributed electrons and positrons, warm ions, and dust grains. The effects of the electron nonextensivity, positron nonextensivity, and fractional parameter on the properties of DIA Gardner wave are investigated. Space fractional Gardner (SFG) equation is derived using the semi inverse technique. An efficient modified G′/G-expansion method is presented to solve the SFG equation. It is found that the amplitude of the DIA Gardner wave increases with an increase in space fractional parameter β $\left(\beta \right)$ and spatial parameter ζ $\left(\zeta \right)$ . On other hands, the DIA Gardner wave shape can be modulated using the space fractional parameter β $\left(\beta \right)$ . Our results may help understand the astrophysical environments such as star magnetospheres, solar flares, and galactic nuclei.

Modeling the spatiotemporal intracellular calcium dynamics in nerve cell with strong memory effects

Calcium signaling in nerve cells is a crucial activity for the human brain to execute a diversity of its functions. An alteration in the signaling process leads to cell death. To date, several attempts registered to study the calcium distribution in nerve cells like neurons, astrocytes, etc. in the form of the integer-order model. In this paper, a fractional-order mathematical model to study the spatiotemporal profile of calcium in nerve cells is assembled and analyzed. The proposed model is solved by the finite element method for space derivative and finite difference method for time derivative. The classical case of the calcium dynamics model is recovered by setting the fractional parameter and that validates the model for classical sense. The numerical computations have systematically presented the impact of a fractional parameter on nerve cells. It is observed that calbindin-D28k provides a significant effect on the spatiotemporal variation of calcium profile due to the amalgamation of the memory of nerve cells. The presence of excess amounts of calbindin-D28k controls the intracellular calcium level and prevents the nerve cell from toxicity.

Magnetohydrodynamic Blood Flow in a Cylindrical Tube with Magnetic Particles: A Time Fractional Model

The present work theoretically investigates the natural convection blood flow as a Brinkman-type fluid with uniformly distributed magnetic particles in a circular cylindrical tube with the applied external magnetic field. The classical model for the blood flow is generalized by using the definition of Caputo time-fractional derivative. The exact solutions are obtained by using the Laplace and Henkel transforms. Unlike the classical model, the obtained general results are expressed in the form of “Lorenzo and Hartley’s” and “Robotnov and Hartley’s” functions. Graphs are plotted to show the effects of different parameters on the blood flow. Furthermore, the velocity and temperature distributions are discussed in terms of memory. The effect of fractional parameter α for a long and short time has also been observed. It is noticed that blood velocity can be controlled using the fractional parameter. It is also found that, for τ > 0 , fluid and particles motion increased, and reverse behavior is observed for τ < 0 . It has been noticed that increasing values of particle mass parameter P m and magnetic parameter M slow down the motion of blood and magnetic particles. These results are helpful for effective drug delivery and regulating blood flow.

String cosmology from fractional action with solitonic NS–NS matter and possibility of an accelerated expanding universe without dark energy

In this study, we discuss string cosmology with solitonic NS–NS matter, which arises when dilaton coupled p-brane gas dominates the universe and is subject to a fractional action motivated from viscosity dissipative effects occurring in the universe. Exact solutions are found from the stationary conditions of the fractional action. It was observed that the universe is non-singular, undergoing accelerated expansion in time and may not be dominated by dark energy because it is strongly affected by dissipations through the fractional parameter α. The numerical ranges of α were obtained using H(z) at the 1σ level for two independent cases: a vacuum energy dominated energy and a non-dominant vacuum energy universe. Our results are in agreement with astronomical observational limits and support both string cosmology and the fractional action cosmology.

Exact Solution of Fractional Convective Casson Fluid Through an Accelerated Plate

Fractional derivative has perfectly adopted to model few physical phenomena such as viscoelasticity of coiling polymers, traffic construction, fluid dynamics and electrical networks. However, the application of the fractional derivatives for describing the physical characteristics of non-Newtonian fluid over a moving plate is still rare. In the present study, the effect of the Caputo fractional derivative on the Casson fluid flow which is induced by an accelerated plate is analytically analysed. The governing equations are initially transformed into dimensionless expressions by using suitable dimensionless variables. Then the Laplace transform method is utilized to calculate the exact solutions for the fractional governing partial differential equations. The obtained solutions are validated by comparing the results for specific case with the existing solutions in the literature. The impact of fractional parameter, Prandtl number, and time on the velocity and temperature profiles are graphically showed and discussed. The results depict that the temperature and velocity increase with the increment of fractional parameter and time. Interestingly, the velocity decreases at region near the plate but is enhanced at the area far away from the plate when the Casson fluid parameter is increased. This study is essential in understanding the factional non-Newtonian fluid flows which is more realistic in nature.

Prospecting black hole thermodynamics with fractional quantum mechanics

This paper investigates whether the framework of fractional quantum mechanics can broaden our perspective of black hole thermodynamics. Concretely, we employ a space-fractional derivative (Riesz in Acta Math 81:1, 1949) as our main tool. Moreover, we restrict our analysis to the case of a Schwarzschild configuration. From a subsequently modified Wheeler–DeWitt equation, we retrieve the corresponding expressions for specific observables. Namely, the black hole mass spectrum, M, its temperature T, and entropy, S. We find that these bear consequential alterations conveyed through a fractional parameter, $$\alpha $$ α . In particular, the standard results are recovered in the specific limit $$\alpha =2$$ α = 2 . Furthermore, we elaborate how generalizations of the entropy-area relation suggested by Tsallis and Cirto (Eur Phys J C 73:2487, 2013) and Barrow (Phys Lett B 808:135643, 2020) acquire a complementary interpretation in terms of a fractional point of view. A thorough discussion of our results is presented.