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Oct 15, 2020Open    AccessArticle

A Fractional Order Model for the Transmission Dynamics of Measles with Vaccination

Nnaemeka S. Aguegboh, Nkem R. Nwokoye, Netochukwu E. Onyiaji, Ogechi R. Amanso, Dominic O. Oranugo
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...
Open Access Library J. Vol.7, 2020
Doi:10.4236/oalib.1106670


May 07, 2020Open    AccessArticle

On the Stability of Duffing Type Fractional Differential Equation with Cubic Nonlinearity

Nnaji Daniel Ugochukwu, Makuochukwu Felix Oguagbaka, Ezenwobodo Somkene Samuel, Nnaemeka Stanley Aguegboh, Onyiaji Netochukwu Ebube
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.
Open Access Library J. Vol.7, 2020
Doi:10.4236/oalib.1106184


Apr 29, 2020Open    AccessArticle

A Novel Iterative Method Based on Bernstein-Adomian Polynomials to Solve Non-Linear Differential Equations

Afaf Nasser Yousif, Ahmed Farooq Qasim
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...
Open Access Library J. Vol.7, 2020
Doi:10.4236/oalib.1106267


Mar 19, 2020Open    AccessArticle

Multi-Derivative Multistep Method for Initial Value Problems Using Boundary Value Technique

Emmanuel A. Areo, Oluwatoyin A. Edwin
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.
Open Access Library J. Vol.7, 2020
Doi:10.4236/oalib.1106063


Apr 10, 2019Open    AccessArticle

The Explicit Fatunla’s Method for First-Order Stiff Systems of Scalar Ordinary Differential Equations: Application to Robertson Problem

Hippolyte Nyengeri, Eugène Ndenzako, Rénovat Nizigiyimana
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
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Open Access Library J. Vol.6, 2019
Doi:10.4236/oalib.1105291


Oct 30, 2018Open    AccessArticle

Correlation of Brownian Motions and Its Impact on a Reinsurer’s Optimal Investment Strategy and Reinsured Proportion under Exponential Utility Maximization and Constant Elasticity of Variance Model

Silas A. Ihedioha
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-
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Open Access Library J. Vol.5, 2018
Doi:10.4236/oalib.1104954


Jun 26, 2018Open    AccessArticle

Solvability of a Class of Operator-Differential Equations of Third Order with Complicated Characteristic on the Whole Real Axis

Abdel Baset I. Ahmed, Mohamed A. Labeeb
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.
Open Access Library J. Vol.5, 2018
Doi:10.4236/oalib.1104631


Dec 19, 2017Open    AccessArticle

On the Solvability of the Boundary-Value Problem for the First Order Operator-Differential Equations with Multiple Characteristics

Mohamed A. Labeeb, Ahmed L. Elbably, Abdel Baset I. Ahmed
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.
Open Access Library J. Vol.4, 2017
Doi:10.4236/oalib.1104155


May 03, 2017Open    AccessArticle

A Deterministic Mathematical Model for Direct and Indirect Transmission Dynamics of Typhoid Fever

Stephen Edward
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
...
Open Access Library J. Vol.4, 2017
Doi:10.4236/oalib.1103493


Nov 02, 2016Open    AccessArticle

About the Integral Equations for Calculation of Green’s Tensor in Elastic Inhomogeneous Medium

Igor Petrovich Dobrovolsky
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.
Open Access Library J. Vol.3, 2016
Doi:10.4236/oalib.1103077


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