Second Order Semilinear Volterra-Type Integro-Differential Equations with Non-Instantaneous Impulses

Fuzzy collocation methods for second- order fuzzy Abel-Volterra integro-differential equations

In this paper we intend to offer new numerical methods to solve the second-order fuzzy Abel-Volterraintegro-differential equations under the generalized $H$-differentiability. The existence and uniqueness of thesolution and convergence of the proposed methods are proved in details and the efficiency of the methods is illustrated through a numerical example.

NON-STANDARD FINITE DIFFERENCE METHOD FOR NUMERICAL SOLUTION OF SECOND ORDER LINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

In this article we have considered a non-standard finite difference method for the solution of second order  Fredholm integro differential equation type initial value problems. The non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the Fredholm integro-differential equation into a system of equations. We have also developed a numerical met...

Existence Results for Fractional Order Mixed Type Functional Integro-differential Equations with Impulses

In this paper, we prove the existence of mild solutions for the semilinear fractional order functional of Volterra-Fredholm type differential equations with impulses in a Banach space. The results are obtained by using the theory of fractional calculus, the analytic semigroup theory of linear operators and the fixed point techniques. ifx

Stability Analysis for Nonlinear Second Order Differential Equations with Impulses∗

In this paper we investigate the impulsive equation { (r(t)x′) + a(t)x + f (t, x, x′) = p(t), t ≥ t0, t 6= tk, x(tk) = ckx(tk − 0), x(tk) = dkx(tk − 0), k = 1, 2, 3, . . . , and establish a couple of criteria to guarantee the equations of this type to possess the stability, including boundedness and asymptotic properties. Some examples are given to illustrate our results and the last one shows ...

MultiPoint BVPs for Second-Order Functional Differential Equations with Impulses