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...

In this ‎article‎‎, ‎an ‎ap‎plied matrix method, which is based on Bernouli Polynomials, has been presented to find approximate solutions of ‎high order ‎Volterra ‎integro-differential‎ equations. Through utilizing this approach, the proposed equations reduce to a system of algebric equations with unknown Bernouli coefficients. A number of numerical ‎illustrations‎ have been ‎solved‎ to ‎assert...

This paper establishes a study on some important latest innovations in the uniqueness of solution for Caputo fractional Volterra-Fredholm integro-differential equations. To apply this, the study uses Banach contraction  principle and Bihari's inequality.  A wider applicability of these techniques are based on their reliability and reduction in the size of the mathematical work.

in this paper, we apply the local fractional laplace transform method (or yang-laplace transform) on volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. the iteration procedure is based on local fractional derivative operators. this approach provides us with a convenient way to find a solution ...

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.

The Laplace transform method is applied to study the semi-Hyers–Ulam–Rassias stability of a Volterra integro-differential equation second order. A general formulated first; then, some particular cases for function from kernel are considered.

In this paper we intend to offer new numerical methods to solve the second-order fuzzy Abel-Volterraintegro-differential equations under the generalized $H$-differentiability. The existence and uniqueness of thesolution and convergence of the proposed methods are proved in details and the efficiency of the methods is illustrated through a numerical example.

Bernstein polynomials have been recently used for the solution of some linear and non-linear differential equations, both partial and ordinary, by Bhatta and Bhatti [1] and Bhatti and Bracken [2]. Also these have been used to solve some classes of inegral equations of both first and second kinds, by Mandal and Bhattacharya [3]. These were further used to solve a Cauchy singular integro-differen...