Analysis and analytical simulation for a biophysical fractional diffusive cancer model with virotherapy using the Caputo operator

In this paper, a biophysical fractional diffusive cancer model with virotherapy is thoroughly analyzed and analytically simulated. The goal of this biophysical model is to represent both the dynamics of cancer development and the results of virotherapy, which uses viruses to target and destroy cancer cells. The Caputo sense is applied to the fractional derivatives. We look at the governing model's existence and uniqueness. For analytical solutions, the Laplace residual power series approach is used. The study investigates the model's dynamic behavior, shedding light on the development of cancer and the effects of virotherapy. The research advances our knowledge of cancer modeling and treatment options. Numerical simulations show the agreement between the analytical results and the related numerical solutions, proving the usefulness of the analytical solution

MHD effects on Casson fluid flow squeezing between parallel plates

We introduce this work by studying the non-Newtonian fluids, which have huge applications in different science fields. We decided to concentrate on taking the time-dependent Casson fluid, which is non-Newtonian, compressed between two flat plates. in fractional form and the magnetohydrodynamic and Darcian flow effects in consideration using the semi-analytical iterative method created by Temimi and Ansari, known as TAM, this method is carefully selected to be suitable for studying the Navier-Stokes model in the modified form to express the studied case mathematically. To simplify the partial differential equations of the system to the nonlinear ordinary differential equation of order four the similarity transformations suggested by Wang (1976) are used. The TAM approach demonstrates a high degree of accuracy, efficiency, and convergence when applied to the resolution of both linear and nonlinear problems, and the results in this article are used to study the effect of the related factors like squeeze number Sq, Casson parameterβ, magnetohydrodynamic parameter Mg and permeability constant Mp and examining the skin friction coefficient effect. The velocity profile is studied numerically, which is tabulated and graphically represented to show and confirm the theoretical study. We can conclude that the success of the proposed method in studying time-dependent Casson fluid, which is non-Newtonian, compressed between two flat plates provides opportunities for additional study and advancements in fluid mechanics using the techniques

Emotional Stability among the Ex-detainees Palestinian Children from Israeli Prisons

The objectives of the study were to identify the emotional stability among the ex-detainees Palestinian children from Israeli prisons. Emotional stability scale was administrated to 299 children using the stratified random sampling method. The findings revealed that the ex-detainees Palestinian children experienced a low level of emotional stability. These results confirmed the traumatic experiences on the personality of the ex-detainees Palestinian children from Israeli prisons. The consequences of the findings for practice are highlighted

A solution for the neutron diffusion equation in the spherical and hemispherical reactors using the residual power series

A novel analytical solution to the neutron diffusion equation is proposed in this study using the residual power series approach for both spherical and hemispherical fissile material reactors. Various boundary conditions are investigated, including zero flux on the boundary, zero flux on the extrapolated boundary distance, and the radiation boundary condition (RBC). The study also shows how two hemispheres with opposing flat faces interact. We give numerical results for the same energy neutrons diffused in pure P239u. By qualitative comparison with the homotopy perturbation method and Bessel function-based solutions, the residual power series method (RPSM) presents accurate series solutions that converge to the exact solutions, as shown in this study. Moreover, numerical results were shown to be improved by the computer implementation of the analytic solutions

Analytical solutions to the coupled fractional neutron diffusion equations with delayed neutrons system using Laplace transform method

The neutron diffusion equation (NDE) is one of the most important partial differential equations (PDEs), to describe the neutron behavior in nuclear reactors and many physical phenomena. In this paper, we reformulate this problem via Caputo fractional derivative with integer-order initial conditions, whose physical meanings, in this case, are very evident by describing the whole-time domain of physical processing. The main aim of this work is to present the analytical exact solutions to the fractional neutron diffusion equation (F-NDE) with one delayed neutrons group using the Laplace transform (LT) in the sense of the Caputo operator. Moreover, the poles and residues of this problem are discussed and determined. To show the accuracy, efficiency, and applicability of our proposed technique, some numerical comparisons and graphical results for neutron flux simulations are given and tested at different values of time $t$ and order $\alpha$ which includes the exact solutions (when $\alpha = 1).$ Finally, Mathematica software (Version 12) was used in this work to calculate the numerical quantities

Using Laplace Residual Power Series Method in Solving Coupled Fractional Neutron Diffusion Equations with Delayed Neutrons System

In this paper, a system of coupled fractional neutron diffusion equations with delayed neutrons was solved efficiently by using a combination of residual power series and Laplace transform techniques, and the anomalous diffusion was considered by taking the non-Gaussian case with different values of fractional parameter α. The Laplace residual power series method (LRPSM) does not require differentiation, conversion, or discretization for the assumed conditions, so the approach is simple and suitable for solving higher-order fractional differential equations. To assure the theoretical results, two different neutron flux initial conditions were presented numerically, where the needed Mathematica codes were performed using essential nuclear reactor cross-section data, and the results for different values of times were tabulated and graphically figured out. Finally, it must be noted that the results align with the Adomian decomposition method

Developing a new approaching technique of homotopy perturbation method to solve two-group reflected cylindrical reactor

The solution of neutron diffusion equation is important to describe the behavior of the neutrons in the nuclear reactors. The essential cylindrical reactor geometry will be studied in this work, where the reactor reflector part is added to the core part to minimize its critical radius, and the neutrons diffuse in two different velocities. The massive results when diversification of the appropriate new approaching technique of homotopy perturbation method (HPM) represent its flexibility and suitability to deal with different nuclear reactor boundary conditions. To assure our results, a comparison with classical results and transport theory data has been achieved which made after needed simplification to one velocity case. The necessary C++ codes using GSL library are accomplished to attain this comparison. Keywords: Neutron diffusion, Homotopy perturbation method, Flux calculation, Critical system, Cylindrical geometry, Reflected reactor, Bessel functio

Solution of different geometries reflected reactors neutron diffusion equation using the homotopy perturbation method

The Homotopy Perturbation Method (HPM) proves continuous efficiency for a long time in solving linear and nonlinear mathematical differential equations and their applications in physical and engineering phenomena. In this work, HPM is applied to formulate new analytic solutions of time-independent neutron diffusion equation for different reflected reactor geometries, which is essential in describing the behaviour of the neutrons in the nuclear reactors. The reflector part is added to the core to minimize the critical dimensions and critical mass too. The results have been compared with canonical calculations, as well as to that taken from transport theory. This comparison has been achieved after computationally applying the developed theory and analytical formulas in numerical experiments. The methodology furnishes the ground for further future research in this field. Keywords: Neutron diffusion, Homotopy perturbation method, Flux calculation, Critical system, Reflected reactor, Bessel functio

Traveling Wave Solutions for Complex Space-Time Fractional Kundu-Eckhaus Equation

In this work, the class of nonlinear complex fractional Kundu-Eckhaus equation is presented with a novel truncated M-fractional derivative. This model is significant and notable in quantum mechanics with good-natured physical characteristics. The motivation for this paper is to construct new solitary and kink wave solutions for the governing equation using the ansatz method. A complex-fractional transformation is applied to convert the fractional Kundu-Eckhaus equation into an ordinary differential equations system. The equilibria of the corresponding dynamical system will be presented to show the existence of traveling wave solutions for the governing model. A novel kink and solitary wave solutions of the governing model are realized by means of the proposed method. In order to gain insight into the underlying dynamics of the obtained solutions, some graphical representations are drawn. For more illustration, several numerical applications are given and analyzed graphically to demonstrate the ability and reliability of the method in dealing with various fractional engineering and physical problems