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This paper presents a comprehensive model of hemodynamic pulsatile flow within the carotid artery, examining both normal conditions and those affected by stenosis. The primary focus lies in visualizing shear stress along the inner walls, aiming to elucidate how stenosis alters blood flow characteristics and subsequently impacts plaque deposition. Utilizing advanced computational fluid dynamics simulations, temporal variations in flow patterns, velocity profiles, and pressure gradients resulting from stenosis are captured, thereby elucidating the mechanical forces exerted on arterial walls. Moreover, this study analyzes the influence of hemodynamic parameters, such as Reynolds number, Womersley number, and arterial geometry, on flow disruption and stagnation points. Such insights are critical in understanding the mechanisms underlying plaque formation and progression. Critical thresholds of shear stress and flow patterns contributing to endothelial dysfunction and atherosclerotic lesion initiation are identified by comparing hemodynamic environments in healthy vs stenotic arteries. The results demonstrate significant differences in hemodynamic characteristics between stenosed and normal arteries, particularly near systolic peaks. Stenosed arteries exhibit notably higher velocities at arterial bifurcations during systole than normal arteries, indicative of altered flow dynamics. In addition, stenosis disrupts flow patterns, leading to vortex formation at locations beyond systolic peaks. Overall, findings from this research advance our understanding of cardiovascular disease pathogenesis and provide valuable insights into the hemodynamic effects of arterial stenosis. [ABSTRACT FROM AUTHOR]

A powerful algorithm is proposed to get the solutions of the time fractional Advection-Diffusion equation(TFADE): ABCD0+,tβu(x,t)=ζuxx(x,t)−κux(x,t)+$^{ABC}\mathcal{D}_{0^+,t}^{\beta}u(x,t) =\zeta u_{xx}(x,t)- \kappa u_x(x,t)+$F(x, t), 0 < β ≤ 1. The time-fractional derivative ABCD0+,tβu(x,t)$^{ABC}\mathcal{D}_{0^+,t}^{\beta}u(x,t)$is described in the Atangana-Baleanu Caputo concept. The basis of our approach is transforming the original equation into a new equation by imposing a transformation involving a fictitious coordinate. Then, a geometric scheme namely the group preserving scheme (GPS) is implemented to solve the new equation by taking an initial guess. Moreover, in order to present the power of the presented approach some examples are solved, successfully.

In this study, we purpose to ensure optical soliton solutions of the nonlinear Schrödinger equation having parabolic and anti-cubic (AC) laws with a weakly non-local nonlinearity by using the new Kudryashov method. As far as we know this model has not been presented and studied before. Furthermore, what differs this study from other studies is, not only obtains a variety of analytical solutions of the examined model but also substantiates the effects of the parabolic and anti-cubic laws with a weakly non-local nonlinearity on soliton behaviour, by choosing the particular soliton forms, which are dark, bright and W-like. Eventually, we depict some of the derived solutions in contour, 2D and 3D diagrams selecting the appropriate values of parameters by means of Matlab to demonstrate the importance of the given model. It is indicated that parabolic and AC parameters taking into consideration the weak non-local contribution have a very remarkable impact on the soliton structure, and the impact alters connected with the parameters and the soliton form. Besides, enabling and retaining the critical balance between the parameters and the soliton form and the interactive relation of the parameters with each other comprises major challenges. [ABSTRACT FROM AUTHOR]

In this paper, we study the oscillation of solutions to a non-linear fractional differential equation with damping term. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. By using a variable transformation, a generalized Riccati transformation, inequalities, and integration average techniquewe establish new oscillation criteria for the fractional differential equation. Several illustrative examples are also given.

In this study, a vibration problem of Euler-Bernoulli beam manufactured with Functionally Graded Material (FGM), which is modelled by fourth-order partial differential equations with variable coefficients, is examined by using the Adomian Decomposition Method (ADM).The method is one of the useful and powerful methods which can be easily applied to linear and nonlinear initial and boundary value problems. As to functionally graded materials, they are composites mixed by two or more materials at a certain rate. This mixture at a certain rate is expressed with an exponential function in order to try to minimize singularities from transition between different surfaces of materials as much as possible. According to the structure of the ADM in terms of initial conditions of the problem, a Fourier series expansion method is used along with the ADM for the solution of simply supported functionally graded Euler-Bernoulli beams. Finally, by choosing an appropriate mixture rate for the material, the results are shown in figures and compared with those of a standard (homogeneous) Euler-Bernoulli beam.

The novel coronavirus SARS-Cov-2 is a pandemic condition and poses a massive menace to health. The governments of different countries and their various prohibitory steps to restrict the virus’s expanse have changed individuals’ communication processes. Due to physical and financial factors, the population’s density is more likely to interact and spread the virus. We establish a mathematical model to present the spread of the COVID-19 in worldwide. In this article, we propose a novel mathematical model (‘SLIIqIhRP’) to assess the impact of using hospitalization, quarantine measures, and pathogen quantity in controlling the COVID-19 pandemic. We analyse the boundedness of the model’s solution by employing the Laplace transform approach to solve the fractional Gronwall’s inequality. To ensure the uniqueness and existence of the solution, we rely on the Picard-Lindelof theorem. The model’s basic reproduction number, a crucial indicator of epidemic potential, is determined based on the greatest eigenvalue of the next-generation matrix. We then employ stability theory of fractional differential equations to qualitatively examine the model. Our findings reveal that both locally and globally, the endemic equilibrium and disease-free solutions demonstrate symptomatic stability. These results shed light on the effectiveness of the proposed interventions in managing and containing the COVID-19 outbreak. [ABSTRACT FROM AUTHOR]