Keywords: Analytic semigroup Banach fixed point theorem Caputo derivative Faedo–Galerkin approximations Nonlocal conditions Neutral fractional differential equation a b s t r a c t This paper is concerned with the approximation of the solution for neutral fractional differential equation with nonlocal conditions in an arbitrary separable Hilbert space H. We study an associated integral equation...

This study presents a Feynman-Kac path-integral implementation for solving the Dirichlet problem for Poisson’s equation. The algorithm is a modified “walk on spheres” (WOS) that includes the FeynmanKac path-integral contribution for the source term. In our approach, we use the Poisson kernel instead of simulating Brownian trajectories in detail to implement the path-integral computation. We der...

This paper develops a modification of the dressing method based on the nonhomoge-neous linear integral equation with integral operator having nonempty kernel. Method allows one to construct systems of multidimensional Partial Differential Equations (PDEs) in the form of differential polynomial in any dimension n. Associated solution space is not full, although it is parameterized by a certain n...

This paper develops a modification of the dressing method based on inhomogeneous linear integral equation with integral operator having nonempty kernel. Method allows one to construct the systems of multidimensional Partial Differential Equations (PDEs) having differential polynomial structure in any dimension n. Associated solution space is not full, although it is parametrized by certain numb...