A New Scheme of the ARA Transform for Solving Fractional-Order Waves-Like Equations Involving Variable Coefficients

The goal of this research is to develop a new,simplified analytical method known as the ARA-residue power series method for obtaining exact-approximate solutions employing Caputo type fractional partial differential equations(PDEs)with variable coefficient.ARA-transform is a robust and highly flexible generalization that unifies several existing transforms.The key concept behind this method is to create approximate series outcomes by implementing the ARA-transform and Taylor’s expansion.The process of finding approximations for dynamical fractional-order PDEs is challenging,but the ARA-residual power series technique magnifies this challenge by articulating the solution in a series pattern and then determining the series coefficients by employing the residual component and the limit at infinity concepts.This approach is effective and useful for solving a massive class of fractional-order PDEs.Five appealing implementations are taken into consideration to demonstrate the effectiveness of the projected technique in creating solitary series findings for the governing equations with variable coefficients.Additionally,several visualizations are drawn for different fractional-order values.Besides that,the estimated findings by the proposed technique are in close agreement with the exact outcomes.Finally,statistical analyses further validate the efficacy,dependability and steady interconnectivity of the suggested ARA-residue power series approach.

The Spherical q-Linear Diophantine Fuzzy Multiple-Criteria Group Decision-Making Based on Differential Measure

Spherical q-linearDiophantine fuzzy sets(Sq-LDFSs)provedmore effective for handling uncertainty and vagueness in multi-criteria decision-making(MADM).It does not only cover the data in two variable parameters but is also beneficial for three parametric data.By Pythagorean fuzzy sets,the difference is calculated only between two parameters(membership and non-membership).According to human thoughts,fuzzy data can be found in three parameters(membership uncertainty,and non-membership).So,to make a compromise decision,comparing Sq-LDFSs is essential.Existing measures of different fuzzy sets do,however,can have several flaws that can lead to counterintuitive results.For instance,they treat any increase or decrease in the membership degree as the same as the non-membership degree because the uncertainty does not change,even though each parameter has a different implication.In the Sq-LDFSs comparison,this research develops the differentialmeasure(DFM).Themain goal of the DFM is to cover the unfair arguments that come from treating different types of FSs opposing criteria equally.Due to their relative positions in the attribute space and the similarity of their membership and non-membership degrees,two Sq-LDFSs formthis preference connectionwhen the uncertainty remains same in both sets.According to the degree of superiority or inferiority,two Sq-LDFSs are shown as identical,equivalent,superior,or inferior over one another.The suggested DFM’s fundamental characteristics are provided.Based on the newly developed DFM,a unique approach tomultiple criterion group decision-making is offered.Our suggestedmethod verifies the novel way of calculating the expert weights for Sq-LDFSS as in PFSs.Our proposed technique in three parameters is applied to evaluate solid-state drives and choose the optimum photovoltaic cell in two applications by taking uncertainty parameter zero.The method’s applicability and validity shown by the findings are contrasted with those obtained using various other existing approaches.To assess its stability and usefulness,a sensitivity analysis is done.

Dynamical Analysis of the Stochastic COVID-19 Model Using Piecewise Differential Equation Technique

Various data sets showing the prevalence of numerous viral diseases have demonstrated that the transmission is not truly homogeneous.Two examples are the spread of Spanish flu and COVID-19.The aimof this research is to develop a comprehensive nonlinear stochastic model having six cohorts relying on ordinary differential equations via piecewise fractional differential operators.Firstly,the strength number of the deterministic case is carried out.Then,for the stochastic model,we show that there is a critical number RS0 that can predict virus persistence and infection eradication.Because of the peculiarity of this notion,an interesting way to ensure the existence and uniqueness of the global positive solution characterized by the stochastic COVID-19 model is established by creating a sequence of appropriate Lyapunov candidates.Adetailed ergodic stationary distribution for the stochastic COVID-19 model is provided.Our findings demonstrate a piecewise numerical technique to generate simulation studies for these frameworks.The collected outcomes leave no doubt that this conception is a revolutionary doorway that will assist mankind in good perspective nature.

New Configurations of the Fuzzy Fractional Differential Boussinesq Model with Application in Ocean Engineering and Their Analysis in Statistical Theory

The fractional-order Boussinesq equations(FBSQe)are investigated in this work to see if they can effectively improve the situation where the shallow water equation cannot directly handle the dispersion wave.The fuzzy forms of analytical FBSQe solutions are first derived using the Adomian decomposition method.It also occurs on the sea floor as opposed to at the functionality.A set of dynamical partial differential equations(PDEs)in this article exemplify an unconfined aquifer flow implication.Thismethodology can accurately simulate climatological intrinsic waves,so the ripples are spread across a large demographic zone.The Aboodh transform merged with the mechanism of Adomian decomposition is implemented to obtain the fuzzified FBSQe in R,R^(n) and(2nth)-order involving generalized Hukuhara differentiability.According to the system parameter,we classify the qualitative features of the Aboodh transform in the fuzzified Caputo and Atangana-Baleanu-Caputo fractional derivative formulations,which are addressed in detail.The illustrations depict a comparison analysis between the both fractional operators under gH-differentiability,as well as the appropriate attributes for the fractional-order and unpredictability factorsσ∈[0,1].A statistical experiment is conducted between the findings of both fractional derivatives to prevent changing the hypothesis after the results are known.Based on the suggested analyses,hydrodynamic technicians,as irrigation or aquifer quality experts,may be capable of obtaining an appropriate storage intensity amount,including an unpredictability threshold.

Simulating the Turbulent Hydrothermal Behavior of Oil/MWCNT Nanofluid in a Solar Channel Heat Exchanger Equipped with Vortex Generators

Re-engineering the channel heat exchangers(CHEs)is the goal of many recent studies,due to their great importance in the scope of energy transport in various industrial and environmental fields.Changing the internal geometry of the CHEs by using extended surfaces,i.e.,VGs(vortex generators),is the most common technique to enhance the efficiency of heat exchangers.This work aims to develop a newdesign of solar collectors to improve the overall energy efficiency.The study presents a new channel design by introducing VGs.The FVM(finite volume method)was adopted as a numerical technique to solve the problem,with the use of Oil/MWCNT(oil/multi-walled carbon nano-tubes)nanofluid to raise the thermal conductivity of the flow field.The study is achieved for a Re number ranging from12×10^(3) to 27×10^(3),while the concentration(φ)of solid particles in the fluid(Oil)is set to 4%.The computational results showed that the hydrothermal characteristics depend strongly on the flow patterns with the presence of VGs within the CHE.Increasing the Oil/MWCNT rates with the presence of VGs generates negative turbulent velocities with high amounts,which promotes the good agitation of nanofluid particles,resulting in enhanced great transfer rates.

Spherical Linear Diophantine Fuzzy Sets with Modeling Uncertainties in MCDM

The existing concepts of picture fuzzy sets(PFS),spherical fuzzy sets(SFSs),T-spherical fuzzy sets(T-SFSs)and neutrosophic sets(NSs)have numerous applications in decision-making problems,but they have various strict limitations for their satisfaction,dissatisfaction,abstain or refusal grades.To relax these strict constraints,we introduce the concept of spherical linearDiophantine fuzzy sets(SLDFSs)with the inclusion of reference or control parameters.A SLDFSwith parameterizations process is very helpful formodeling uncertainties in themulti-criteria decisionmaking(MCDM)process.SLDFSs can classify a physical systemwith the help of reference parameters.We discuss various real-life applications of SLDFSs towards digital image processing,network systems,vote casting,electrical engineering,medication,and selection of optimal choice.We show some drawbacks of operations of picture fuzzy sets and their corresponding aggregation operators.Some new operations on picture fuzzy sets are also introduced.Some fundamental operations on SLDFSs and different types of score functions of spherical linear Diophantine fuzzy numbers(SLDFNs)are proposed.New aggregation operators named spherical linear Diophantine fuzzy weighted geometric aggregation(SLDFWGA)and spherical linear Diophantine fuzzy weighted average aggregation(SLDFWAA)operators are developed for a robust MCDM approach.An application of the proposed methodology with SLDF information is illustrated.The comparison analysis of the final ranking is also given to demonstrate the validity,feasibility,and efficiency of the proposed MCDM approach.

Computational Analysis of the Effect of Nano Particle Material Motion on Mixed Convection Flow in the Presence of Heat Generation and Absorption

The present study is concerned with the physical behavior of the combined effect of nano particle material motion and heat generation/absorption due to the effect of different parameters involved in prescribed flow model.The formulation of the flow model is based on basic universal equations of conservation of momentum,energy and mass.The prescribed flow model is converted to non-dimensional form by using suitable scaling.The obtained transformed equations are solved numerically by using finite difference scheme.For the analysis of above said behavior the computed numerical data for fluid velocity,temperature profile,and mass concentration for several constraints that is mixed convection parameterλt,modified mixed convection parameterλc,Prandtl number Pr,heat generation/absorption parameterδ,Schmidt number Sc,thermophoresis parameter Nt,and thermophoretic coefficient k are sketched in graphical form.Numerical results for skin friction,heat transfer rate and the mass transfer rate are tabulated for various emerging physical parameters.It is reported that in enhancement in heat,generation boosts up the fluid temperature at some positions of the surface of the sphere.As heat absorption parameter is decreased temperature field increases at position X=π/4 on the other hand,no alteration at other considered circumferential positions is noticed.

A New Idea of Fractal-Fractional Derivative with Power Law Kernel for Free Convection Heat Transfer in a Channel Flow between Two Static Upright Parallel Plates

Nowadays some new ideas of fractional derivatives have been used successfully in the present research community to study different types of mathematical models.Amongst them,the significant models of fluids and heat or mass transfer are on priority.Most recently a new idea of fractal-fractional derivative is introduced;however,it is not used for heat transfer in channel flow.In this article,we have studied this new idea of fractal fractional operators with power-law kernel for heat transfer in a fluid flow problem.More exactly,we have considered the free convection heat transfer for a Newtonian fluid.The flow is bounded between two parallel static plates.One of the plates is heated constantly.The proposed problem is modeled with a fractal fractional derivative operator with a power-law kernel and solved via the Laplace transform method to find out the exact solution.The results are graphically analyzed via MathCad-15 software to study the behavior of fractal parameters and fractional parameter.For the influence of temperature and velocity profile,it is observed that the fractional parameter raised the velocity and temperature as compared to the fractal operator.Therefore,a combined approach of fractal fractional explains the memory of the function better than fractional only.

New Computation of Unified Bounds via a More General Fractional Operator Using Generalized Mittag-Leffler Function in the Kernel

In the present case,we propose the novel generalized fractional integral operator describing Mittag-Leffler function in their kernel with respect to another function Φ.The proposed technique is to use graceful amalgamations of the Riemann-Liouville(RL)fractional integral operator and several other fractional operators.Meanwhile,several generalizations are considered in order to demonstrate the novel variants involving a family of positive functions n(n∈N)for the proposed fractional operator.In order to confirm and demonstrate the proficiency of the characterized strategy,we analyze existing fractional integral operators in terms of classical fractional order.Meanwhile,some special cases are apprehended and the new outcomes are also illustrated.The obtained consequences illuminate that future research is easy to implement,profoundly efficient,viable,and exceptionally precise in its investigation of the behavior of non-linear differential equations of fractional order that emerge in the associated areas of science and engineering.

Compact Ceshro Operators from Spaces H（p,q,u） to H（p, q, v）

Let μ and v be normal functions and let Tg be the extended Ceshso operator in terms of the symbol g. In this paper, we will characterize those g so that Tg is bounded （or compact） from mixed norm spaces H（p, q, μ） to H（p, q, v） in the unit ball of C^n, Furthermore, as applications, some analogous results are also given on weighted Bergman spaces and Dirichlet type spaces.

Entropy generation applications in flow of viscoelastic nanofluid past a lubricated disk in presence of nonlinear thermal radiation and Joule heating

Entropy generation is the loss of energy in thermodynamical systems due to resistive forces,diffusion processes,radiation effects and chemical reactions.The main aim of this research is to address entropy generation due to magnetic field,nonlinear thermal radiation,viscous dissipation,thermal diffusion and nonlinear chemical reaction in the transport of viscoelastic fluid in the vicinity of a stagnation point over a lubricated disk.The conservation laws of mass and momentum along with the first law of thermodynamics and Fick’s law are used to discuss the flow,heat and mass transfer,while the second law of thermodynamics is used to analyze the entropy and irreversibility.The numbers of independent variables in the modeled set of nonlinear partial differential equations are reduced using similarity variables and the resulting system is numerically approximated using the Keller box method.The effects of thermophoresis,Brownian motion and the magnetic parameter on temperature are presented for lubricated and rough disks.The local Nusselt and Sherwood numbers are documented for both linear and nonlinear thermal radiation and lubricated and rough disks.Graphical representations of the entropy generation number and Bejan number for various parameters are also shown for lubricated and rough disks.The concentration of nanoparticles at the lubricated surface reduces with the magnetic parameter and Brownian motion.The entropy generation declines for thermophoresis diffusion and Brownian motion when lubrication effects are dominant.It is concluded that both entropy generation and the magnitude of the Bejan number increase in the presence of slip.The current results present many applications in the lubrication phenomenon,heating processes,cooling of devices,thermal engineering,energy production,extrusion processes etc.

MHD flow study of viscous fluid through a complex wavy curved surface due to biomimetic propulsion under porosity and second-order slip effects

The steady laminar flow of viscous fluid from a curved porous domain under a radial magnetic field is considered.The fluid flow by a curved domain is due to peristaltic waves present at the boundary walls.The whole analysis is based on porosity(Darcy number)effects.Moreover,the effects of second-order slip on the rheology analysis are also discussed.Due to the complex nature of the flow regime,we have governed the rheological equations by using curvilinear coordinates in the fixed frame.The physical influence of magnetic(Hartmann number)and porosity(Darcy number)parameters on the rheological features of peristaltic transportation are argued in detailed(in the wave frame).Additionally,in the current study,the complex wavy pattern on both boundary walls of the channel is used.The whole rheological study is based on ancient,but medically valid,assumptions of creeping phenomena and long wavelength assumptions.Analytical solutions of the governing equations are obtained by using the simple integration technique in Mathematica software 11.0.The core motivation of the present analysis is to perceive the physical influence of embedded parameters,such as the dimensionless radius of the curvature parameter,magnetic parameter,porosity parameter,different amplitude ratios of complex peristaltic waves,first-and second-order slip parameters,on the axial velocity,pressure gradient,local wall shear stress,tangential component of the extra-stress tensor,pumping and trapping phenomena.