This paper deals with the exponential stability of a class of nonlinear delay-integrodifferential equations of the form ẋ(t) = f ( t, x(t), x(t − τ1(t)), ∫ t t−τ2(t) g(t, s, x(s))ds ) , t ≥ t0, where τi(t) > 0 for i = 1, 2 and t ≥ t0. The stability relation between ordinary and delay-integro-differential equations is given. It is shown under some suitable conditions that a delay-integro-differe...

We discuss the approximate controllability of nonlinear fractional integro-differential system under the assumptions that the corresponding linear system is approximately controllable. Using the fixed-point technique, fractional calculus and methods of controllability theory, a new set of sufficient conditions for approximate controllability of fractional integro-differential equations are form...

This paper is concerned with the numerical stability of implicit Runge-Kutta methods for nonlinear neutral Volterra delay-integro-differential equations with constant delay. Using a Halanay inequality generalized by Liz and Trofimchuk, we give two sufficient conditions for the stability of the true solution to this class of equations. Runge-Kutta methods with compound quadrature rule are consid...

The method of generalized quasilinearization technique when is applied to the nonlinear integrodifferential equations of Volterra type, gives two sequences of linear integro-differential equations with solutions monotonically and quadratically convergent to the solution of nonlinear equation. In this paper we employ step-by-step collocation method to solve the linear equations numerically and t...

in this paper, the numerical algorithms for solving ‘fuzzy ordinary differential equations’ are considered. a scheme based on the 4th order runge-kutta method is discussed in detail and it is followed by a complete error analysis. the algorithm is illustrated by solving some linear and nonlinear fuzzy cauchy problems.

In this paper, a Bernoulli pseudo-spectral method for solving nonlinear fractional Volterra integro-differential equations is considered. First existence of a unique solution for the problem under study is proved. Then the Caputo fractional derivative and Riemman-Liouville fractional integral properties are employed to derive the new approximate formula for unknown function of the problem....

In this paper, we exhibit two methods to numerically solve the fractional integro differential equations and then proceed to compare the results of their applications on different problems. For this purpose, at first shifted Jacobi polynomials are introduced and then operational matrices of the shifted Jacobi polynomials are stated. Then these equations are solved by two methods: Caputo fractio...

In this note, we prove the periodic homogenization for a family of nonlinear nonlocal “elliptic” equations with oscillatory coefficients. Such equations include, but are not limited to Bellman equations for the control of pure jump processes and the Isaacs equations for differential games of pure jump processes. The existence of an effective equation and convergence the solutions of the family ...

We prove Hölder regularity results for a class of nonlinear elliptic integro-differential operators with integration kernels whose ellipticity bounds are strongly directionally dependent. These results extend those in [9] and are also uniform as the order of operators approaches 2.