In this paper, a generalized mathematical model of spread of infectious disease as SIRS epidemic model is considered as a nonlinear system of differential equation. We prove that for positive initial conditions the resulting equivalence system has positive solution and under some hypothesis, this system with initial positive condition, has a positive $T$-periodic solution which is globally asym...

In this paper, an improved predictor-corrector methods (IPC) to solve fuzzy differential equation under generalized differentiability are discussed. The methods proposed here are based on generalized characterization theorem. Using the Generalized Characterization we can translate a fuzzy differential equation into two ODE systems. Also, the convergence and stability of the proposed methods are...

We study the generalized half-linear second order differential equation and the associated Riccati type differential equation. We introduce the concepts of minimal and principal solutions of these equations and using these concepts we prove a new conjugacy criterion for the generalized half-linear equation.

The principles of superposition and separation variables are used here in order to investigate the analytical solutions a certain transient heat conduction equation. structure temperature appropriations heat-transfer distributions summed up for straight mix results by means Fourier-Bessel arrangement exponential type investigated partial differential

‎This paper obtains the exact solutions of the wave equation as a second-order partial differential equation (PDE)‎. ‎We are going to calculate polynomial and non-polynomial exact solutions by using Lie point symmetry‎. ‎We demonstrate the generation of such polynomial through the medium of the group theoretical properties of the equation‎. ‎A generalized procedure for polynomial solution is pr...

In this paper, the method of transmutation operators is used to construct an exact solution Goursat problem for a fourth-order hyperbolic equation with singular Bessel operator. We emphasise that in many other papers and monographs fractional Erdélyi-Kober are as integral operators, but our approach them additional new properties important applications. Specifically, it extends its applications...

Suppose that d ∈ N and p > 0. In this paper, we study the generalized Bessel functions for the surface {v ∈ Rd : |v|p = 1}, introduced by D.St.P. Richards. We derive a recurrence relation for these functions and utilize a series representation to relate them to the classical symmetric functions. These generalized Bessel functions are symmetric with respect to the action of the hyperoctahedral g...

In this paper, we consider the non-homogeneous wave equation generated by Bessel operator. We prove existence and uniqueness of solution The representation is given. obtained a priori estimates in Sobolev type space. This problem was firstly considered work M. Assal [1] setting Bessel-Kingman hypergroups. technique used based on convolution theorem related estimates. Here, use different approac...

The discrete Painlevé III equation is investigated based on the bilinear formalism. It is shown that it admits the solutions expressed by the Casorati determinant whose entries are given by the discrete Bessel function. Moreover, based on the observation that these discrete Bessel functions are transformed to the q-Bessel functions by a simple variable transformation, we present a q-difference ...