In the classical non-life insurance models, the capital reserve of an insurance company increases at a constant rate and decreases by downward jumps. We consider a generalization of this model by supposing that a fixed portion of the capital reserve...
In this paper, we study a dynamically consistent numerical method for the approximation of a nonlinear integro-differential equation modeling an epidemic with age of infection. The discrete scheme is based on direct quadrature methods with Gregory co...
In this paper, we consider an integro-differential model of nerve conduction which presents the propagation of impulses in the nerve’s membranes. First, we approximate the original problem via cellular nonlinear networks (CNNs). The dynamics of...
In this paper, we prove the existence and uniqueness of solutions for a nonlocal, fourth-order integro-differential equation that models electrostatic MEMS with parallel metallic plates by exploiting a well-known implicit function theorem on the topo...
Mathematics and physics are deeply interconnected. In fact, physics relies on mathematical tools like calculus and differential equations. The aim of this article is to introduce tempered Riemann–Liouville (RL) fractional operators and their pr...
In this study, we focus on the stability analysis of the RLC model by employing differential equations with Hadamard fractional derivatives. We prove the existence and uniqueness of solutions using Banach’s contraction principle and Schaefer&rs...
The work is dedicated to mathematical modelling of random diffusion flows of admixture particles in a two-phase stratified strip with stochastic disposition of phases and random thickness of inclusion-layers. The study of such models are especially i...
The model of the spread of the coronavirus pandemic in the form of a system of integro-differential equations is studied. We focus our consideration on the number of hospitalized patients, i.e., on the needs of the system regarding hospital beds that...
This paper presents a comprehensive mathematical analysis of a novel compartmental model describing the dynamics of dispersed water pollutants and their interaction with two distinct host populations. The model is formulated as a system of integro-di...
In this paper, we propose an efficient numerical method for solving an initial boundary value problem for a coupled system of equations consisting of a nonlinear parabolic partial integro-differential equation and an elliptic equation with a nonlinea...
In this paper, we consider the M/G/1 stochastic clearing queueing model in a three-phase environment, which is described by integro-partial differential equations (IPDEs). Our first result is semigroup well-posedness for the dynamic system. Utilizing...
This article deals with the implementation of fuzzy differential transform method for solving a system of nonlinear fuzzy integro-differential equations. This system appears in a model of biological species living together. Though the differential tr...
This work illustrates the application of the “First-Order Features Adjoint Sensitivity Analysis Methodology for Neural Integro-Differential Equations of Fredholm-Type” (1st-FASAM-NIDE-F) and the “Second-Order Features Adjoint Sensit...
We consider a simple model for QCD dynamics in which DGLAP integro-differential equation may be solved analytically. This is a gauge model which possesses dominant evolution of gauge boson (gluon) distribution and in which the gauge coupling does not...
This work presents the mathematical frameworks of the “First-Order Features Adjoint Sensitivity Analysis Methodology for Neural Integro-Differential Equations of Volterra-Type” (1st-FASAM-NIDE-V) and the “Second-Order Features Adjoi...
Influenza, often referred to as the flu, is an extremely contagious respiratory illness caused by influenza viruses, impacting populations globally with significant health consequences annually. A hallmark of influenza is its seasonal patterns, influ...
Differential models, numerical methods and computer simulations play a fundamental role in applied sciences. Since most of the differential models inspired by real world applications have no analytical solutions, the development of numerical methods...
In the present paper, we study a diauxic growth that can be generated by a class of model at the mesoscopic scale. Although the diauxic growth can be related to the macroscopic scale, similarly to the logistic scale, one may ask whether models on mes...
The high-order finite difference method for option pricing is one of the most popular numerical algorithms. Therefore, it is of great significance to study its convergence rate. Based on the relationship between this algorithm and the trinomial tree...
Recently, different mathematical frameworks of the thermostatted kinetic theory approach have been proposed for the modeling of complex systems. In particular, thermostatted kinetic frameworks have been employed for the modeling and time evolution of...
At present, a significant part of oil is extracted from difficult-to-develop reservoirs with low permeability. Hydraulic fracturing is one of the most important methods of production stimulation. Scientific articles do not describe the connections be...
This paper is devoted to the investigation of the ruin probability in the risk model with stochastic premiums where dividends are paid according to a multi-layer dividend strategy. We obtain an exponential bound for the ruin probability and investiga...
This paper deals with the ruin problem of an insurance company investing its capital reserve in a risky asset with the price dynamics given by a conditional geometric Brownian motion whose parameters depend on a Markov process describing random varia...
Periodic traveling waves are observed in various brain activities, including visual, motor, language, sleep, and so on. There are several neural field models describing periodic waves assuming nonlocal interaction, and possibly, inhibition, time dela...
The mathematical modeling of multicellular systems is an important branch of biophysics, which focuses on how the system properties emerge from the elementary interaction between the constituent elements. Recently, mathematical structures have been p...
We investigate the well-posedness of an initial boundary value problem for the Kelvin–Voigt–Brinkman–Forchheimer equations with memory and variable viscosity under a non-homogeneous Dirichlet boundary condition. A theorem about the...
In this article, a scalar nonlinear integro-differential equation of second order and a non-linear system of integro-differential equations with infinite delays are considered. Qualitative properties of solutions called the global asymptotic stabilit...
Fractional integro-differential equations arise in the mathematical modeling of various physical phenomena like heat conduction in materials with memory, diffusion processes, etc. In this manuscript, we prove the existence of mild solution for Sobole...
In this article, a class of scalar nonlinear integro-differential equations of first order with fading memory is investigated. For the considered fading memory problem, we discuss the effects of the memory over all the values of the parameter in the...
Integro-differential equations involving Volterra and Fredholm operators (VFIDEs) are used to model many phenomena in science and engineering. Nonlocal boundary conditions are more effective, and in some cases necessary, because they are more accurat...
There is great focus on phenomena that depend on their past history or their past state. The mathematical models of these phenomena can be described by differential equations of a self-referred type. This paper is devoted to studying the solvability...
This study is devoted to studying the existence and uniqueness of solutions for Hadamard implicit fractional differential equations with generalized Hadamard fractional integro-differential boundary conditions by utilizing the contraction principle o...
In this paper the model of infection diseases by Marchuk is considered. Mathematical questions which are important in its study are discussed. Among them there are stability of stationary points, construction of the Cauchy matrices of linearized mode...
An integrodifferential model formulated in terms of the electric vector potential is developed for the 3D numerical modeling of the electromagnetic field in superconducting bulks, for AC losses evaluation. The Newton Raphson method is applied to acce...
Recent developments have shown that the widely used simplified differential model of Eringen’s nonlocal elasticity in nanobeam analysis is not equivalent to the corresponding and initially proposed integral models, the pure integral model and t...
First, we develop a direct operator method for solving boundary value problems for a class of nth order linear Volterra–Fredholm integro-differential equations of convolution type. The proposed technique is based on the assumption that the Volt...
This study addresses a magneto-viscoelasticity problem, considering the one-dimensional case. The system under investigation is given by the coupling a non-linear partial differential equation with a linear integro-differential equation. The system m...
Fractional calculus, which deals with the concept of fractional derivatives and integrals, has become an important area of research, due to its ability to capture memory effects and non-local behavior in the modeling of real-world phenomena. In this...
The memory means an existence of output (response, endogenous variable) at the present time that depends on the history of the change of the input (impact, exogenous variable) on a finite (or infinite) time interval. The memory can be described by th...
In this paper, we study the perturbed risk model with a threshold dividend strategy and proportional investment. The insurance companies are allowed to invest their surplus in a financial market consisting of a risk-free asset and a risky asset in fi...
Modeling of impurity diffusion processes in a multiphase randomly inhomogeneous body is performed using the Feynman diagram technique. The impurity diffusion equations are formulated for each of the phases separately. Their random boundaries are subj...
This paper presents exact solutions for the nonlinear bending problem, the buckling loads, and postbuckling configurations of a perfect and an imperfect bioinspired helicoidal composite beam with a linear rotation angle. The beam is embedded on an el...
In this paper, the existence of optimal solutions for problems governed by differential equations involving feedback controls is established for when the problem must account for a Volterra-type distributed delay and is subject to the action of impul...
The modeling of fuzzy fractional integro-differential equations is a very significant matter in engineering and applied sciences. This paper presents a novel treatment algorithm based on utilizing the fractional residual power series (FRPS) method to...
As a crucial modeling tool for stochastic financial markets, the Lévy risk model effectively characterizes the evolution of risks during enterprise operations. Through dynamic evaluation and quantitative analysis of risk indicators under speci...
This work presents a projection method based on Vieta–Lucas polynomials and an effective approach to solve a Cauchy-type fractional integro-differential equation system. The suggested established model overcomes two linear equation systems. We...
In this research article, we demonstrate the generalized expansion method to investigate nonlinear integro-partial differential equations via an efficient mathematical method for generating abundant exact solutions for two types of applicable nonline...
In this paper, a dual risk model under constant force of interest is considered. The ruin probability in this model is shown to satisfy an integro-differential equation, which can then be written as an integral equation. Using the collocation method,...
This paper presents an analytical model for the hereditary vibrations of a coupled circular plate system interconnected by viscoelastic creep layers. The system is represented as a discrete-continuous chain of thin, isotropic plates with time-depende...
This work presents the “First-Order Features Adjoint Sensitivity Analysis Methodology for Neural Integro-Differential Equations of Fredholm-Type” (1st-FASAM-NIDE-F) and the “Second-Order Features Adjoint Sensitivity Analysis Methodo...
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