Resolvent, Natural, and Sumudu Transformations: Solution of Logarithmic Kernel Integral Equations with Natural Transform

In this paper, the resolvent of an integral equation was found with natural transform which is a new transformation which converged to Laplace and Sumudu transformations, and the result was confirmed by the Sumudu transform. At the same time, a solution to the first type of logarithmic kernel Volterra integral equations has been produced by the natural transform

On the degree of approximation of function belonging to the Lipschitz class by (C,2)(E,1)

In this paper, we obtained a theorem on the degree of approximation of functions belonging to the Lipschitz class by (C,2)(E,1) product means of its Fourier series

Analysing of Tuberculosis in Turkey through SIR, SEIR and BSEIR Mathematical Models

Since mathematical models play a key role in investigating the dynamics of infectious diseases, many mathematical models for these diseases are developed. In this paper, it is aimed to determine the dynamics of Tuberculosis (TB) in Turkey, how much it will affect the future and the impact of vaccine therapy on the disease. For this purpose, three mathematical models (SIR, SEIR and BSEIR) in the literature are considered for the case of Turkey. The model parameters are obtained with TB reported data from 2005 to 2015 by using the least square method. The obtained results revealed that the basic reproduction ratio for all three models is less than 1. Moreover, the stability analysis of the models and sensitivity analysis of the model parameters are presented and discussed. Finally, the accuracy of results for all three models is compared and the effect of the vaccination rate is discussed. © 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group

Special functions in transferring of energy; a specific case: "Airy function"

Analysis of transferring of transient signals along time-harmonic waveguide modes consists of two main parts. The first one is a modal basis problem. The second one is a modal amplitude problem. Surplus of energy could be observed in process of the signal transferring. In this study, time-domain waveguide modes' surplus of energy is represented. Surplus of energy for the waveguide time-domain waveguide modes are presented via Airy function. The previous works are reviewed for energy and surplus of energy of time-domain modes in the waveguides