In this letter, the numerical scheme of nonlinear Volterra-Fredholm integro-differential equations is proposed in a reproducing kernel Hilbert space (RKHS). The method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satised. The nonlinear terms are replaced by its Taylor series. In this technique, the nonlinear Volterra-Fredholm integro...

Modeling continuous dynamical systems from discretely sampled observations is a fundamental problem in data science. Often, such dynamics are the result of non-local processes that present an integral over time. As such, these modeled with Integro-Differential Equations (IDEs); generalizations differential equations comprise both and component. For example, brain not accurately by since their b...

In this paper we provide three equivalent expressions for ruin probabilities in a Cramér-Lundberg model with gamma distributed claims. The results are solutions of integro-differential equations, derived by means of (inverse) Laplace transforms. All the three formulas have infinite series forms, two involving Mittag-Leffler functions and the third one involving moments of the claims distributio...

In this work, we conduct a comparative study among the combine Laplace transform and modied Adomian decomposition method (LMADM) and two traditional methods for an analytic and approximate treatment of special type of nonlinear Volterra integro-differential equations of the second kind. The nonlinear part of integro-differential is approximated by Adomian polynomials, and the equation is reduce...

We study fine boundary regularity properties of solutions to fully nonlinear elliptic integro-differential equations of order 2s, with s 2 .0; 1/. We consider the class of nonlocal operators L L0, which consists of infinitesimal generators of stable Lévy processes belonging to the class L0 of Caffarelli–Silvestre. For fully nonlinear operators I elliptic with respect to L , we prove that soluti...

In this paper, a multipoint boundary value problem for systems of integro-differential equations with involution has been studied. To solve the studied problem, parameterization method is used. Based on parametrization method, decomposed into two parts, i.e., Cauchy and system linear equations. Necessary sufficient conditions unique solvability are determined.

The infinite-genus limit of the KdV–Whitham equations is derived. The limit involves special scaling for the associated spectral surface such that the integrated density of states remains finite as N →∞ (the thermodynamic type limit). The limiting integro-differential system describes slow evolution of the density of states and can be regarded as the kinetic equation for soliton gas.  2003 Els...