MHD Maxwell Fluid with Heat Transfer Analysis under Ramp Velocity and Ramp Temperature Subject to Non-Integer Differentiable Operators

The main focus of this study is to investigate the impact of heat generation/absorption with ramp velocity and ramp temperature on magnetohydrodynamic(MHD)time-dependent Maxwell fluid over an unbounded plate embedded in a permeable medium.Non-dimensional parameters along with Laplace transformation and inversion algorithms are used to find the solution of shear stress,energy,and velocity profile.Recently,new fractional differential operators are used to define ramped temperature and ramped velocity.The obtained analytical solutions are plotted for different values of emerging parameters.Fractional time derivatives are used to analyze the impact of fractional parameters(memory effect)on the dynamics of the fluid.While making a comparison,it is observed that the fractional-order model is best to explain the memory effect as compared to classical models.Our results suggest that the velocity profile decrease by increasing the effective Prandtl number.The existence of an effective Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity.The incremental value of the M is observed for a decrease in the velocity field,which reflects to control resistive force.Further,it is noted that the Atangana-Baleanu derivative in Caputo sense(ABC)is the best to highlight the dynamics of the fluid.The influence of pertinent parameters is analyzed graphically for velocity and energy profile.Expressions for skin friction and Nusselt number are also derived for fractional differential operators.

Dynamical Analysis of Radiation and Heat Transfer on MHD Second Grade Fluid

Convective flow is a self-sustained flow with the effect of the temperature gradient.The density is non-uniform due to the variation of temperature.The effect of the magnetic flux plays a major role in convective flow.The process of heat transfer is accompanied by a mass transfer process;for instance,condensation,evaporation,and chemical process.Due to the applications of the heat and mass transfer combined effects in a different field,the main aim of this paper is to do a comprehensive analysis of heat and mass transfer of MHD unsteady second-grade fluid in the presence of ramped boundary conditions near a porous surface.The dynamical analysis of heat transfer is based on classical differentiation with no memory effects.The non-dimensional form of the governing equations of the model is developed.These are solved by the classical integral(Laplace)transform technique/method with the convolution theorem and closed-form solutions are attained for temperature,concentration,and velocity.The physical aspects of distinct parameters are discussed via graph to see the influence on the fluid concentration,velocity,and temperature.Our results suggest that the velocity profile decrease by increasing the Prandtl number.The existence of a Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity.Furthermore,to validate our results,some results are recovered from the literature.

Fractional Analysis of Viscous Fluid Flow with Heat and Mass Transfer Over a Flexible Rotating Disk

An unsteady viscous fluid flow with Dufour and Soret effect,which results in heat and mass transfer due to upward and downward motion of flexible rotating disk,has been studied.The upward or downward motion of non rotating disk results in two dimensional flow,while the vertical action and rotation of the disk results in three dimensional flow.By using an appropriate transformation the governing equations are transformed into the system of ordinary differential equations.The system of ordinary differential equations is further converted into first order differential equation by selecting suitable variables.Then,we generalize the model by using the Caputo derivative.The numerical result for the fractional model is presented and validated with Runge Kutta order 4 method for classical case.The compared results are presented in Table and Figures.It is concluded that the fractional model is more realistic than that of classical one,because it simulates the fluid behavior at each fractional value rather than the integral values.

Modeling the Spread of Tuberculosis with Piecewise Differential Operators

Very recently,a new concept was introduced to capture crossover behaviors that exhibit changes in patterns.The aimwas tomodel real-world problems exhibiting crossover from one process to another,for example,randomness to a power law.The concept was called piecewise calculus,as differential and integral operators are defined piece wisely.These behaviors have been observed in the spread of several infectious diseases,for example,tuberculosis.Therefore,in this paper,we aim at modeling the spread of tuberculosis using the concept of piecewise modeling.Several cases are considered,conditions under which the unique system solution is obtained are presented in detail.Numerical simulations are performed with different values of fractional orders and density of randomness.

Fractional Analysis of Dynamical Novel COVID-19 by Semi-Analytical Technique

This study employs a semi-analytical approach,called Optimal Homotopy Asymptotic Method(OHAM),to analyze a coronavirus(COVID-19)transmission model of fractional order.The proposed method employs Caputo’s fractional derivatives and Reimann-Liouville fractional integral sense to solve the underlying model.To the best of our knowledge,this work presents the first application of an optimal homotopy asymptotic scheme for better estimation of the future dynamics of the COVID-19 pandemic.Our proposed fractional-order scheme for the parameterized model is based on the available number of infected cases from January 21 to January 28,2020,in Wuhan City of China.For the considered real-time data,the basic reproduction number is R0≈2.48293 that is quite high.The proposed fractional-order scheme for solving the COVID-19 fractional-order model possesses some salient features like producing closed-form semi-analytical solutions,fast convergence and non-dependence on the discretization of the domain.Several graphical presentations have demonstrated the dynamical behaviors of subpopulations involved in the underlying fractional COVID-19 model.The successful application of the scheme presented in this work reveals new horizons of its application to several other fractional-order epidemiological models.

Analysis of Mathematics and Numerical Pattern Formation in Superdiffusive Fractional Multicomponent System

In this work,we examine the mathematical analysis and numerical simulation of pattern formation in a subdiffusive multicomponents fractional-reactiondiffusion system that models the spatial interrelationship between two preys and predator species.The major result is centered on the analysis of the system for linear stability.Analysis of the main model reflects that the dynamical system is locally and globally asymptotically stable.We propose some useful theorems based on the existence and permanence of the species to validate our theoretical findings.Reliable and efficient methods in space and time are formulated to handle any space fractional reaction-diffusion system.We numerically present the complexity of the dynamics that are theoretically discussed.The simulation results in one,two and three dimensions show some amazing scenarios.

A numerical study of the nonlinear fractional mathematical model of tumor cells in presence of chemotherapeutic treatment

Cancer belongs to the class of discascs which is symbolized by out of control cells growth.These cells affect DNAs and damage them.There exist many treatments avail-able in medical science as radiation therapy,targeted therapy,surgery,palliative care and chemotherapy.Cherotherapy is one of the most popular treatments which depends on the type,location and grade of cancer.In this paper,we are working on modeling and prediction of the effect of chemotherapy on cancer cells using a fractional differen-tial equation by using the differential operator in Caputos sense.The presented model depicts the interaction between tumor,norrnal and immune cells in a tumor by using a system of four coupled fractional partial differential equations(PDEs).For this system,initial conditions of tumor cells and dimensions are taken in such a way that tumor is spread out enough in size and can be detected easily with the clinical machines.An operational matrix method with Genocchi polynomials is applied to study this system of fractional PDFs(FPDEs).An operational matrix for fract.ional differentiation is derived.Applying the collocation method and using this matrix,the nonlinear system is reduced to a system of algebraic equations,which can be solved using Newton iteration method.The salient features of this paper are the pictorial presentations of the numerical solution of the concerned equation for different particular cases to show the effect of fractional exponent on diffusive nature of immune cells,tumor cells,normal cells and chemother-apeutic drug and depict the interaction among immune cells,normal cells and tumor cells in a tumor site.

New lump, lump-kink, breather waves and other interaction solutions to the (3+1)-dimensional soliton equation

This study investigates the (3+1)-dimensional soliton equation via the Hirota bilinear approach and symbolic computations. We successfully construct some new lump, lump-kink, breather wave, lump periodic, and some other new interaction solutions. All the reported solutions are verified by inserting them into the original equation with the help of the Wolfram Mathematica package. The solution’s visual characteristics are graphically represented in order to shed more light on the results obtained. The findings obtained are useful in understanding the basic nonlinear fluid dynamic scenarios as well as the dynamics of computational physics and engineering sciences in the related nonlinear higher dimensional wave fields.

Conservatory of Kaup-Kupershmidt Equation to the Concept of Fractional Derivative with and without Singular Kernel

Making use of the traditional Caputo derivative and the newly introduced Caputo-Fabrizio deriva- tive with fractional order and no singular kernel, we extent the nonlinear Kaup-Kupershmidt to the span of fractional calculus. In the analysis, different methods of fixed-point theorem together with the concept of piccard L-stability are used, allowing us to present the existence and uniqueness of the exact solution to models with both versions of derivatives. Finally, we present techniques to perform some numerical simulations for both non-linear models and graphical simulations are provided for values of the order α = 1.00; 0.90. Solutions are shown to behave similarly to the standard well-known traveling wave solution of Kaup-Kupershmidt equation.