We provide existence, uniqueness and stability results for affine stochastic Volterra equations with L1-kernels jumps. Such arise as scaling limits of branching processes in population genetics self-exciting Hawkes mathematical finance. The strategy we adopt the existence part is based on approximations using L2-kernels combined a general result. Most importantly, establish weak duality argumen...

In this paper, we present a new computational method to solve Volterra integral equations of the first kind based on Bernstein polynomials. In this method, using operational matrices turn the integral equation into a system of equations. The computed operational matrices are exact and new. The comparisons show this method is acceptable. Moreover, the stability of the proposed method is studied.

We will apply the successive approximation method forproving the Hyers--Ulam stability of a linear integral equation ofthe second kind.

This article proposes an optimal method for approximate answer of stochastic Ito-Voltrra integral equations, via rationalized Haar functions and their stochastic operational matrix of integration. Stochastic Ito-voltreea integral equation is reduced to a system of linear equations. This scheme is applied for some examples. The results show the efficiency and accuracy of the method.

A method is used to solve the Fredholm-Volterra integral equation of the first kind in the space L2(Ω)×C(0,T ),Ω = {(x,y) : √ x2+y2 ≤ a}, z = 0, and T <∞. The kernel of the Fredholm integral term considered in the generalized potential form belongs to the class C([Ω]×[Ω]), while the kernel of Volterra integral term is a positive and continuous function that belongs to the class C[0,T ]. Also in...

We extend the new approach introduced in [24] and [25] for dealing with stochastic Volterra equations using ideas of Rough Path theory prove global existence uniqueness results. The main idea this is simple: Instead iterated integrals a path comprising data necessary to solve any equation driven by that path, now integral convolutions kernel comprise said data. This leads corresponding abstract...

It has been shown that a normal S-iterative method converges to the solution of a mixed type Volterra-Fredholm functional nonlinear integral equation. Furthermore, a data dependence result for the solution of this integral equation has been proven.

this paper presents some results concerning the existence of solutions for a functional integral equation of volterra type in two variables, via measure of noncompactness. two examples are included to illustrate the main result.