Oct 15, 2020Open AccessArticle
In this paper, the fractional order model was adopted to describe the dynamics of measles and to establish how the virus that causes measles is transmitted as well as how to mitigate the conditions that cause the spread. We showed the existence of the equilibrium states. The threshold parameter of the model was evaluated in terms of parameters in the model using the next generation matrix approach. We provided the conditions for the stability of the disease free and the endemic equilibrium point...
May 07, 2020Open AccessArticle
The purpose of this paper is to study the stability of nonlinear fractional Duffing equation where , by analysing the eigenvalues generated from the system of the given differential equation. Graphical results furthermore show the effect of the damping and nonlinear parameter on the system. Our contribution relies on its application to the choice of hard/soft spring in the mechanism of shock absorbers.
Apr 29, 2020Open AccessArticle
In this paper, a new iterative formula for solving ordinary and partial nonlinear differential equations is derived based on the combination between Bernstein’s polynomial and the Adomian decomposition formula. The solution of the differential equations has been transformed into iterative formulas that find the solution directly without the need to convert it into a non-linear system of equations and solving it by other numerical methods that require considerable time and effort. The obtained re...
Mar 19, 2020Open AccessArticle
The second derivative method which is A-stable is derived using Interpolation Collocation approach. The continuous method obtained are used to generate the main method and complementary methods to solve initial value problems of ordinary differential equation via boundary value technique. Numerical result obtained via the methods shows that the new method can compete with the existing ones in the literature.
Apr 10, 2019Open AccessArticle
Ordinary differential equations (ODEs) are among the most important mathe-matical tools used in producing models in the physical sciences, biosciences, chemical sciences, engineering and many more fields. This has motivated re-searchers to provide efficient numerical methods for solving such equations. Most of these types of differential models are stiff, and suitable numerical methods have to be used to simulate the solutions. Th
Oct 30, 2018Open AccessArticle
This work investigated a reinsurer’s optimal investment strategy and the pro-portion he accepted for reinsurance under proportional reinsurance and expo-nential utility preference in the cases where the Brownian motions were corre-lated and where they did not correlate. The reinsurer invested in a market in which the price process of the risky asset is governed by constant elasticity of variance (CEV) model. The required Hamilton-
Jun 26, 2018Open AccessArticle
On the whole real axis, we
demonstrate sufficient conditions of regular solvability of third order
operator-differential equations with complicated characteristics. These
conditions were formulated only by the operator coefficients of the equation.
In addition, by the principal part of the equation, the norms of the operators
of intermediate derivative were estimated.
Dec 19, 2017Open AccessArticle
In this paper, a class of operator-differential
equation of the first order with multiple characteristics is considered, for
which the initial boundary value problem on the semi-axis is well-posed and
uniquely solvable in the Sobolev space.
May 03, 2017Open AccessArticle
Improvements in sanitation and the provision of
clean drinking water led to the elimination of typhoid fever from developed
countries in the beginning of the 20th century. However, Salmonella typhi and paratyphi remain a major source of morbidity and mortality in many
developing countries toda
Nov 02, 2016Open AccessArticle
The scheme of creation of systems of the
integro-differential equations for evaluation of Green’s function in
non-uniform elastic boundless medium is described. The summand with singularity
is allocated. The isotropic medium with constant coefficient of Poisson and unidimensional
inhomogeneous isotropic medium are considered.