in this paper, we give an analytical approximate solution for an integro- differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. the homotopy analysis method (ham) is used for solving this equation. several examples are given to reconfirm the efficiency of these algorithms. the results of applying this procedure...

Abstract The Laplace transform method is applied in this article to study the semi-Hyers-Ulam-Rassias stability of a Volterra integro-differential equation order n, with convolution-type kernel. This kind extends original Hyers-Ulam whose originated 1940. A general integral formulated first, and then some particular cases (polynomial function exponential function) for from kernel are considered.

In this study, a fractional nonlinear mixed integro-differential equation (Fr-NMIDE) is presented and has general discontinuous kernel based on position time space. Conditions of the existence uniqueness solution provided through principal form integral equation, Banach fixed point theorem. After applying properties integral, Fr-NMIDE conformed to Volterra–Hammerstein (V-HIE) second kind, with ...

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.

Integro-differential polynomials are a novel generalization of the well-known differential polynomials extensively used in differential algebra [17]. They were introduced in [29] as a kind of universal extensions of integro-differential algebras and have recently been applied in a confluence proof [34] for the rewrite system underlying the so-called “integro-differential operators”. In this pap...

We analyse the asymptotic behaviour of integro-differential equations modelling N populations in interaction, where interactions are modelled by non-local terms involving linear combinations of the total number of individuals in each population. These models have already been shown to be suitable for the modelling of drug resistance in cancer. They also generalise the usual Lotka-Volterra ordin...

In this research, the finite difference method is used to solve initial value problem of linear first order Volterra-Fredholm integro-differential equations with singularity. By using implicit rules and composite numerical quadrature rules, scheme established on a Shishkin mesh. The stability convergence proposed are analyzed two examples solved display advantages presented technique.

In this paper the one-dimensional two-phase Stefan problem is studied analytically leading to a system of non-linear Volterra-integral-equations describing heat distribution in each phase. For unified transform method has been employed which provides via global relation, by these problems can be solved using integral representations. To do this, underlying partial differential equation rewritte...