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This paper presents the problem of natural vibration of a two-stage hydraulic cylinder subjected to Euler compression load. The considered hydraulic cylinder is freely supported at both of its ends. The linear vibration problem of the telescopic hydraulic cylinder is based on the kinetic stability criterion using Hamilton’s principle and the Bernoulli-Euler theory. The stiffness of the guide and sealing...
It is observed that in some money exchange operations, every n-variable mean M applied by two market analysts who are acting in different countries should be self reciprocally conjugate. The main result says that the only homogeneous weighted quasi-arithmetic mean satisfying this condition is the weighted geometric mean. In the context of invariance of the geometric mean with respect to the arithmetic-harmonic...
Within this work, we discuss the existence of solutions for a coupled system of linear fractional differential equations involving Caputo-Fabrizio fractional orders. We prove the existence and uniqueness of the solution by using the Picard-Lindel ̈of method and fixed point theory. Also, to compute an approximate solution of problem, we utilize the Adomian decomposition method (ADM), as this method...
In this article, we present a novel hybrid approach, by combining the Sawi transform with the homotopy perturbation method, to achieve the approximate and analytic solutions of nonlinear fractional differential equations (ODE as well as PDE) using the time-fractional Caputo derivative. The proposed algorithm is faster and simple compared to other iterative methods. The Sawi transform is used along...
The purpose of the research is to prepare a mathematical and numerical model for the phenomenon of heat transfer during cryopreservation. In the paper, two popular methods, slow freezing and vitrification, are compared. Furthermore, the basic model of thermal processes is supplemented by the phenomenon of phase transitions. To determine the temperature distribution during cryopreservation processes,...
On a Riemannian manifold, two differential operators: the gradient and the divergence are defined and investigated in the bundle of alternating differential forms of any degree with values in a vector bundle. Several algebraic, analytic and geometric properties of the two operators are derived. The vector character of the gradient on forms turns out to be a source of possible applications.
In fractional calculus, the fractional differential equation is physically and theoretically important. In this article an efficient numerical process has been developed. Numerical solutions of the time fractional fourth order reaction diffusion equation in the sense of Caputo derivative is obtained by using the implicit method, which is a finite difference method and is developed by increasing the...
In this work, we present a posteriori error estimates for the Euler-Bernoulli beam theory with inexact flexural stiffness representation. This is an important subject in practice because beams with non-uniform flexural stiffness are frequently modeled using a mesh of elements with constant stiffness. The error estimates obtained in this work are validated by means of two numerical examples. The estimates...
The paper focuses on the numerical modeling of the three-dimensional solidification process of steel using the finite element method (FEM). The model includes and discusses the formation of shrinkage cavities and the influence of the solid phase content on the feeding of the casting through the riser. The analysis assumed a critical value of the solid phase content, at which the transport of liquid...
A composite plate (matrix and reinforcing elements) under conditions of plane deformation is considered. According to the elastic properties, the material of the plate is considered orthotropic with uniformly distributed defects-cracks that do not interact with each other. The geometric characteristics of defects are statistically independent random variables – the half-length and the orientation...
In this paper, we obtain some closed form series solutions for the time fractional diffusion-wave equation (TFDWE) with the generalized time-fractional Caputo derivative (GTFCD) associated with a source term in polar coordinates. These solutions are found using generalized Laplace and Hankel transforms. We obtained the closed form series solutions in the form of the Polygamma function. The effect...
We give some properties of Schramm functions; among others, we prove that the family of all continuous piecewise linear functions defined on a real interval I is contained in the space ΦBV (I) of functions of bounded variation in the sense of Schramm. Moreover, we show that the generating function of the corresponding Nemytskij composition operator acting between Banach spaces CΦBV (I) of continuous...
A mathematical model is developed to study the characteristics of blood flowing through an arterial segment in the presence of a single and a couple of stenoses. The governing equations accompanied by an appropriate choice of initial and boundary conditions are solved numerically by Taylor Galerkin’s time-stepping equation, and the numerical stability is checked. The pressure, velocity, and stream...
The generalized Korteweg-de Varies-Zakharov-Kuznetsov equation (gKdV-ZK) in (3+1)-dimension has been investigated in this research. This model is used to elucidate how a magnetic field affects the weak ion-acoustic wave in the field of plasma physics. To deftly analyze the wide range of wave structures, we utilized the modified extended tanh and the extended rational sinh-cosh methods. Hyperbolic,...
Reaction-diffusion equations are vitally important due to their role in developing sturdy models in various scientific fields. In the present work, we address an algorithm of the Daftardar-Gejji and Jafari method for solving the nonlinear functional equations of the form ψ = f +L(ψ) + N(ψ). Further, we employ this algorithm to solve Caputo derivative-based time-fractional Cauchy reaction-diffusion...
The colonoscopic electrosurgical polypectomy is a very popular surgical procedure in which the colon polyps are removed. In this work, the mathematical description of the electrical and thermal processes proceeding during this procedure has been proposed. The mathematical model contains the specification of the considered domain’s geometry, the system of the partial differential equations that governs...
This paper examines a third-order fractional partial differential equation (FPDE) in the Caputo sense. The Theta difference method (TDM) is utilized to investigate the problem, and a first-order difference scheme is developed. Stability estimates are obtained by applying the Von Neumann analysis method. A test problem is presented as an application, and numerical results are obtained using Matlab...
We show that every operator with memory acting between Banach spaces CΦBV(I) of continuous functions of bounded variation in the sense of Schramm defined on a compact interval I of a real axis, is a Nemytskij composition operator with the continuous generating function. Moreover, some consequences for uniformly bounded operators with memory will be given. As a by-product, we obtain that a Banach space...
The present study investigates heat and mass transport phenomena associated with the MHD flow of micropolar fluid over a vertically stretched Riga plate under the action of a uniform magnetic field applied parallel to the plate. The objective of the study is to analyze Soret and Dufour effects on this physical situation in the presence of chemical reaction. The governing partial differential equations...
This paper presents a numerical solution of the heat advection equation in a two dimensional domain using the Discontinuous Galerkin Method (DGM). The advection equation is widely used in heat transfer problems, particularly in the field of fluid dynamics. The discontinuous Galerkin method is a numerical technique that allows for the solution of partial differential equations using a piecewise polynomial...
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