Related papers: Abstract non-scalar Volterra difference equations
This study investigates the existence and uniqueness of solutions to Volterra integral equations with discontinuous kernels in both linear and nonlinear cases. The problem is two-dimensional, and the collocation method is employed to…
The exact and approximate solutions of singular integro-differential equations relating to the problems of interaction of an elastic thin finite or infinite non-homogeneous patch with a plate are considered, provided that the materials of…
In this paper, we present a fractional spectral collocation method for solving a class of weakly singular Volterra integro-differential equations (VDIEs) with proportional delays and cordial operators. Assuming the underlying solutions are…
Wavelets are a powerful new mathematical tool which offers the possibility to treat in a natural way quantities characterized by several length scales. In this article we will show how wavelets can be used to solve partial differential…
Nonlinear fractional differential equations have gained a significant place in mathematical physics. Finding the solutions to these equations has emerged as a field of study that has attracted a lot of attention lately. In this work, semi…
In this work, we study the initial value problem associated with an abstract integrodifferential equation in interpolation scales. We prove local-in-time existence, uniqueness, continuation, and a blow-up alternative for regular mild…
Using direct variational method we consider the existence of non-spurious solutions to the following Dirichlet problem $\ddot{x}\left( t\right) =f\left( t,x\left( t\right) \right) $, $x\left( 0\right) =x\left( 1\right) =0 $ where $f:\left[…
We discuss a numerical algorithm for solving nonlinear integro-differential equations, and illustrate our findings for the particular case of Volterra type equations. The algorithm combines a perturbation approach meant to render a…
Integrable fractional equations such as the fractional Korteweg-deVries and nonlinear Schr\"odinger equations are key to the intersection of nonlinear dynamics and fractional calculus. In this manuscript, the first discrete/differential…
We investigate stochastic Volterra equations and their limiting laws. The stochastic Volterra equations we consider are driven by a Hilbert space valued \Levy noise and integration kernels may have non-linear dependence on the current state…
We present a nonlinear partial difference equation defined on a square which is obtained by combining the Miura transformations between the Volterra and the modified Volterra differential-difference equations. This equation is not symmetric…
We discuss the application of variational methods, based on non-smooth critical point theory, to a general class of partial differential inclusions.
The Volterra calculus is a simple and powerful pseudodifferential tool for inverting parabolic equations and it has also found many applications in geometric analysis. On the other hand, an important property in the theory of…
Non-point invertible transformations are completely described for difference equations on the quad-graph and for their differential-difference analogues. As an illustration, these transformations are used to construct new examples of…
We study Euler-type discrete-time schemes for the rough Heston model, which can be described by a stochastic Volterra equation (with non-Lipschtiz coefficient functions), or by an equivalent integrated variance formulation. Using weak…
The Volterra lattice equations are completely integrable and possess bi-Hamiltonian structure. They are integrated using partitioned Lobatto IIIA-B methods which preserve the Poisson structure. Modified equations are derived for the…
We give a unified interpretation of confluences, contiguity relations and Katz's middle convolutions for linear ordinary differential equations with polynomial coefficients and their generalization to partial differential equations. The…
We study the correct solvability of an abstract integro-differential equations in Hilbert space generalizing integro-differential equations arising in the theory of viscoelastisity. The equations under considerations are the abstract…
In the present paper, firstly, we consider the Volterra integral equation of second type for a remainder term in an asymptotic formula of an arithmetic function which satisfies some special conditions and obtained a solution of the…
The work in this paper is four-fold. Firstly, we introduce an alternative approach to solve fractional ordinary differential equations as an expected value of a random time process. Using the latter, we present an interesting numerical…