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Solving First-Order Differential Equations of Z-Numbers’ Initial Value Using Radial Basic Function
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International Journal of Differential Equations publishes research on differential equations, and related integral equations, from all scientists who use differential equations as tools within their own discipline.
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International Journal of Differential Equations maintains an Editorial Board of practicing researchers from around the world, to ensure manuscripts are handled by editors who are experts in the field of study.
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Second-Order Elliptic Equation with Singularities
On the compact Riemannian manifold of dimension , we study the existence and regularity of nontrivial solutions for nonlinear second-order elliptic equation with singularities. At the end, we give a geometric application of the above singular equation.
Exact Solutions for the Conformable Space-Time Fractional Zeldovich Equation with Time-Dependent Coefficients
The aim of this paper is to improve a sub-equation method to solve the space-time fractional Zeldovich equation with time-dependent coefficients involving the conformable fractional derivative. As result, we obtain three families of solutions including the hyperbolic, trigonometric, and rational solutions. These solutions may be helpful to explain several phenomena in chemistry, including the combustion process. The study shows that the used method is effective and reliable and can be utilized as a substitution to construct new solutions of different types of nonlinear conformable fractional partial differential equations (NFPDEs) with variable coefficients.
Multiple Solutions for Elliptic -Kirchhoff-Type Potential Systems in Unbounded Domains
In this paper, we establish the existence of at least three weak solutions for a parametric double eigenvalue quasi-linear elliptic -Kirchhoff-type potential system. Our approach is based on a variational method, and a three critical point theorem is obtained by Bonano and Marano.
An Optimal Control for a Two-Dimensional Spatiotemporal SEIR Epidemic Model
In this paper, we present an application of optimal control theory on a two-dimensional spatial-temporal SEIR (susceptible, exposed, infected, and restored) epidemic model, in the form of a partial differential equation. Our goal is to minimize the number of susceptible and infected individuals and to maximize recovered individuals by reducing the cost of vaccination. In addition, the existence of the optimal control and solution of the state system is proven. The characterization of the control is given in terms of state function and adjoint. Numerical results are provided to illustrate the effectiveness of our adopted approach.
An Improved Collocation Approach of Euler Polynomials Connected with Bernoulli Ones for Solving Predator-Prey Models with Time Lag
This paper deals with an approach to obtaining the numerical solution of the Lotka–Volterra predator-prey models with discrete delay using Euler polynomials connected with Bernoulli ones. By using the Euler polynomials connected with Bernoulli ones and collocation points, this method transforms the predator-prey model into a matrix equation. The main characteristic of this approach is that it reduces the predator-prey model to a system of algebraic equations, which greatly simplifies the problem. For these models, the explicit formula determining the stability and the direction is given. Numerical examples illustrate the reliability and efficiency of the proposed scheme.
Stability and Global Sensitivity Analysis for an Agree-Disagree Model: Partial Rank Correlation Coefficient and Latin Hypercube Sampling Methods
In this paper, we present a new mathematical model that describes agree-disagree opinions during polls. We first present the model and its different compartments. Then, we use the next-generation matrix method to compute thresholds of equilibrium stability. We perform the stability analysis of equilibria to determine under which conditions these equilibrium points are stable or unstable. We show that the existence and stability of these equilibria are controlled by the calculated thresholds. Finally, we also perform several computational and statistical experiments to validate the theoretical results obtained in this work. To study the influence of various parameters on these thresholds and to identify the most influential parameters, a global sensitivity analysis is carried out based on the partial rank correlation coefficient method and the Latin hypercube sampling.
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