In this paper, author proves the algorithms for the existence as well as the approximation of solutions to a couple of periodic boundary value problems of nonlinear first order ordinary integro-differential equations using operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration method embodied in the recent hybrid fixed point theorems of D...

Beginning from the creator of integro-differential equations Volterra, many scientists have investigated these equations. Classic method for solving integro-differential equations is the quadratures method that is successfully applied up today. Unlike these methods, Makroglou applied hybrid methods that are modified and generalized in this paper and applied to the numerical solution of Volterra...

This article concerns boundary-value problems of first-order nonlinear impulsive integro-differential equations: y′(t) + a(t)y(t) = f(t, y(t), (Ty)(t), (Sy)(t)), t ∈ J0, ∆y(tk) = Ik(y(tk)), k = 1, 2, . . . , p,

A new perturbation method called the homotopy perturbation method (HPM) [1 – 4] was proposed by Ji-Huan He in 1999, which is a coupling of the traditional perturbation method and homotopy in topology. The traditional perturbation methods are based on assuming a small parameter, and the approximate solutions obtained by those methods, in most cases, are valid only for small values of the small p...

We consider the elastic stress near a hole with corners in an infinite plate under biaxial stress. The elasticity problem is formulated using complex Goursat functions, resulting set of singular integro-differential equations on boundary. boundary integral are solved numerically Chebyshev collocation method which augmented by fractional power term, derived asymptotic analysis corner region, to ...

in this letter, the numerical scheme of nonlinear volterra-fredholm integro-differential equations is proposed in a reproducing kernel hilbert space (rkhs). the method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satised. the nonlinear terms are replaced by its taylor series. in this technique, the nonlinear volterra-fredholm integr...

In this paper, we consider some boundary value problems (BVP) for fractional order partial differential equations ‎(FPDE)‎ with non-local boundary conditions. The solutions of these problems are presented as series solutions analytically via modified Mittag-Leffler functions. These functions have been modified by authors such that their derivatives are invariant with respect to fractional deriv...

The Adomian’s decomposition method (ADM) is a solution method with a wide range of applications including the solution of algebraic, differential, integral and integro-differential equations or system of equations. This method was first introduced by Adomian [1, 2] in the beginning of the 1980’s. In this method the solution is considered as an rapidly converging, infinite series. The convergenc...