Related papers: Integro-differential equations with delays: A pert…
This paper is an attempt to solve an important class of hypersingular integral equations of the second kind. To this end, we apply a new weighted and modified perturbation method which includes some special cases of the Adomian…
The main purpose of this paper is to provide a summary of the fundamental methods for analyzing delay differential equations arising in biology and medicine. These methods are employed to illustrate the effects of time delay on the behavior…
The $\mu$-neutral linear fractional multi-delayed differential nonhomogeneous system with noncommutative coefficient matrices is introduced. The novel $\mu$-neutral multi-delayed perturbation of Mittag-Leffler type matrix function is…
This paper establishes the equivalence between systems described by a single first-order hyperbolic partial differential equation and systems described by integral delay equations. System-theoretic results are provided for both classes of…
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…
In this work, we consider the regularity property of stochastic convolutions for a class of abstract linear stochastic retarded functional differential equations with unbounded operator coefficients. We first establish some useful estimates…
Delay Gronwall inequality with a weakly singular kernel has been a subject of interest in various mathematical studies. In this article, we will delve into the consideration of this inequality and its application in the study continuity of…
In this paper, we investigate the existence and uniqueness of solutions and derive the Ulam--Hyers--Mittag--Leffler stability results for impulsive implicit $\Psi$--Hilfer fractional differential equations with time delay. It is…
In this article we discuss the requirements needed in order to characterise the solution space of perturbed linear integro-differential Volterra convolution equations. We highlight in general how the pointwise behaviour of perturbation…
In general, adding a stochastic perturbation to a differential equation possessing an invariant manifold destroys the invariance as far as the It\^o formalism is used. In this article, we propose an invariantization method for perturbations…
Comparison principles for Volterra equations play a role analogous to maximum principles in PDEs: they provide positivity and stability information on the solution and allow one to control the output of bounded inputs. In the continuous…
In the present study, a numerical method, perturbation-iteration algorithm (shortly PIA), have been employed to give approximate solutions of nonlinear fractional-integro differential equations (FIDEs). Comparing with the exact solution,…
Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine…
We study the existence and uniqueness of solutions of a nonlinear integro-differential problem which we reformulate introducing the notion of the decreasing rearrangement of the solution. A dimensional reduction of the problem is obtained…
A new integration scheme, combining the stability and the precision of usual pseudo-spectral codes with the locality of finite differences methods, is introduced. It turns out to be particularly suitable for the study of front and…
In this paper, the stability of $\theta$-methods for delay differential equations is studied based on the test equation $y'(t)=-A y(t) + B y(t-\tau)$, where $\tau$ is a constant delay and $A$ is a positive definite matrix. It is mainly…
This paper studies the problem of stability of a parameterized delay differential equations (DDE see equation (0.1)). After discretizing the DDE (0.1), we show that the problem can be equivalently casted into a semi-definite programming…
An integro-differential equation, modeling dynamic fractional order viscoelasticity, with a Mittag-Leffler type convolution kernel is considered. A discontinuous Galerkin method, based on piecewise constant polynomials is formulated for…
Fuzzy partial integro-differential equations have a major role in the fields of science and engineering. In this paper, we propose the solution of fuzzy partial Volterra integro-differential equation with convolution type kernel using fuzzy…
Ordinary differential equations of the second order with one constant delay are considered in this paper. An analytical representation of the solution is obtained using the method of steps.