A linear partial integro-differential equation is solved both numerically and analytically using variational iteration method. This equation typically arises in viscoelasticity and other areas. The analytic solution is represented by an infinite series.

Abstract: In this paper, motivated by the research on qualitative properties of solutions for fractional differential-integro equations, some new Gronwall-Bellman type inequalities in two independent variables are established. Based on these inequalities, explicit bounds for unknown functions concerned are derived. As for applications, we apply the inequalities established to research boundedne...

A model potential for two-particle relativistic systems is investigated in the framework of Poincare-invariant quantum mechanics (or relativistic Hamiltonian dynamics). The potential considered allows to reduce the main integro-differential equation of Poincare-invariant quantum mechanics to the equation analogous to the radial equation and have analytical solution for relativistic bound system...

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We will prove the well-posedness of certain second order ordinary and partial integro-differential equations with an integral term of the form t ∫ 0 m(φ(t−s))φ̇(s) ds, wherem is given and φ is the solution. The new aspect is the dependence of the kernel on the solution. In addition, for the ordinary integro-differential equation, the asymptotic behaviour of the solution is described for some ker...

In this work first we consider a physiologically structured population model with a distributed recruitment process. That is, our model allows newly recruited individuals to enter the population at all possible individual states, in principle. The model can be naturally formulated as a first order partial integro-differential equation, and it has been studied extensively. In particular, it is w...

In our symbolic approach to boundary problems for linear ordinary differential equations we use the algebra of integro-differential operators as an algebraic analogue of differential, integral and boundary operators (Section 2). They allow to express the problem statement (differential equation and boundary conditions) as well as the solution operator (an integral operator called “Green’s opera...

the purpose of this paper is to study the fuzzy fractional differentialequations. we prove that fuzzy fractional differential equation isequivalent to the fuzzy integral equation and then using this equivalenceexistence and uniqueness result is establish. fuzzy derivative is considerin the goetschel-voxman sense and fractional derivative is consider in theriemann liouville sense. at the end, we...

The global stability behavior of a non-autonomous neutral functional integro-differential equation is studied. A sufficient condition for every solution of this equation to tend to zero is given.

We are interested in the long time behaviour of the positive solutions of the Cauchy problem involving the integro-differential equation