Fractional model of MHD blood flow in a cylindrical tube containing magnetic particles

In recent years, the use of magnetic particles for biomedicine and clinical therapies has gained considerable attention. Unique features of magnetic particles have made it possible to apply them in medical techniques. These techniques not only provide minimal invasive diagnostic tools but also transport medicine within the cell. In recent years, MRI, drug supply to infected tissue, Hyperthermia are more enhanced by the use of magnetic particles. The present study aims to observe heat and mass transport through blood flow containing magnetic particles in a cylindrical tube. Furthermore, the magnetic field is applied vertically to blood flow direction. The Caputo time fractional derivative is used to model the problem. The obtained partial fractional derivatives are solved using Laplace transform and finite Hankel transform. Furthermore, the effect of various physical parameters of our interest has also been observed through various graphs. It has been noticed that the motion of blood and magnetic particles is decelerated when the particle mass parameter and the magnetic parameter are increased. These findings are important for medicine delivery and blood pressure regulation.

Catalan Transform of k -Balancing Sequences

In this work, the Catalan transformation (CT) of k -balancing sequences, B k , n n ≥ 0 , is introduced. Furthermore, the obtained Catalan transformation C B k , n n ≥ 0 was shown as the product of lower triangular matrices called Catalan matrices and the matrix of k -balancing sequences, B k , n n ≥ 0 , which is an n × 1 matrix. Apart from that, the Hankel transform is applied further to calculate the determinant of the matrices formed from C B k , n n ≥ 0 .

Hankel Transform of the Type 2 (p,q)-Analogue of r-Dowling Numbers

In this paper, type 2 (p,q)-analogues of the r-Whitney numbers of the second kind is defined and a combinatorial interpretation in the context of the A-tableaux is given. Moreover, some convolution-type identities, which are useful in deriving the Hankel transform of the type 2 (p,q)-analogue of the r-Whitney numbers of the second kind are obtained. Finally, the Hankel transform of the type 2 (p,q)-analogue of the r-Dowling numbers are established.

Comparison between two analytical solutions of advection-diffusion equation using separation technique and Hankel transform

On this work, contrast between two analytical and numerical solutions of the advection-diffusion equation has been completed. We use the method of separation of variables, Hankel transform and Adomian numerical method. Also, Fourier rework, and square complement methods has been used to clear up the combination. The existing version is validated with the information sets acquired at the Egyptian Atomic Energy Authority test of radioactive Iodine-135 (I135) at Inshas in unstable conditions. On this model the wind speed and vertical eddy diffusivity are taken as characteristic of vertical height in the techniques and crosswind eddy diffusivity as function in wind speed. These values of predicted and numerical concentrations are comparing with the observed data graphically and statistically.

Full-Vectorial Fiber Mode Solver Based on a Discrete Hankel Transform

It is crucial to be time and resource-efficient when enabling and optimizing novel applications and functionalities of optical fibers, as well as accurate computation of the vectorial field components and the corresponding propagation constants of the guided modes in optical fibers. To address these needs, a novel full-vectorial fiber mode solver based on a discrete Hankel transform is introduced and validated here for the first time for rotationally symmetric fiber designs. It is shown that the effective refractive indices of the guided modes are computed with an absolute error of less than 10−4 with respect to analytical solutions of step-index and graded-index fiber designs. Computational speeds in the order of a few seconds allow to efficiently compute the relevant parameters, e.g., propagation constants and corresponding dispersion profiles, and to optimize fiber designs.

Catalan transform of the incomplete Jacobsthal numbers and incomplete generalized Jacobsthal polynomials

We introduce the Catalan transform of the Incomplete Jacobsthal numbers. We apply the Hankel transform to the Catalan transforms of these numbers. We calculate determinants of matrixes formed with [Formula: see text]by using Hankel transform. Then we define the incomplete [Formula: see text]-Jacobsthal polynomials. Then we examine the recurrence relation and some properties of these polynomials.