In this paper, the existence and uniqueness of the solution of a nonlinear fully fuzzy implicit integro-differential equation arising in the field of fluid mechanics is investigated. First, an equivalency lemma is presented by which the problem understudy is converted to the two different forms of integral equation depending on the kind of differentiability of the solution. Then, the conditions...

In this article, the recurrence relations and shift operators for multivariate Hermite polynomials are derived using factorization approach. Families of differential equations, including differential, integro–differential, partial obtained these operators. The Volterra integral is also discovered.

*Correspondence: [email protected] 1Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, 10520, Thailand 2Centre of Excellence in Mathematics, CHE, Sri Ayutthaya Road, Bangkok, 10400, Thailand Full list of author information is available at the end of the article Abstract This paper is concerned with the existence of extremal solution...

A proof of high-order convergence of three deterministic particle methods for the convectiondiffusion equation in two dimensions is presented. The methods are based on discretizations of an integro-differential equation in which an integral operator approximates the diffusion operator. The methods differ in the discretization of this operator. The conditions for convergence imposed on the kerne...