In this paper, we investigate the semi-Hyers–Ulam–Rassias stability of a Volterra integro-differential equation order I with convolution type kernel. To purpose Laplace transform is used. The results obtained show that holds for problems formulated various functions: exponential and polynomial functions. An important aspect appears in form studied symmetry product.

A new and effective direct method to determine the numerical solution of specific nonlinear Volterra-Fredholm integral and integro-differential equations is proposed. The method is based on vector forms of block-pulse functions (BPFs). By using BPFs and its operational matrix of integration, an integral or integro-differential equation can be transformed to a nonlinear system of algebraic equat...

This paper concerns the implementation of orthogonal polynomials using Galerkin method for solving Volterra integro-differential and Fredholm equations. The constructed are used as basis functions in assumed solution employed. Numerical examples some selected problems provided results obtained show that with performed creditably well terms absolute errors obtained.

Abstract In this paper, we analyze various classes of multi-dimensional ( ? , c )-almost periodic type functions with values in complex Banach spaces. The main structural properties and characterizations for the introduced are presented. We provide certain applications our abstract theoretical results to Volterra integro-differential equations, as well.

In this paper, we propose a new algorithm for constructing an integral model of nonlinear dynamic system the “input–output” type in form quadratic segment Volterra integro-power series (polynomial). We consider nonparametric identification models using physically realizable piecewise linear test signals time domain. The advantage presented approach is to obtain explicit formulas calculating tra...

The homotopy analysis method [1, 2], is developed to search the accurate asymptotic solutions of nonlinear problems. This technique has been successfully applied to many nonlinear problems such as the viscous flows of non-Newtonian fluids [3, 4], the Korteweg-de Vries-type equations [5, 6], nonlinear heat transfer [7, 8], finance problems [9, 10], Riemann problems related to nonlinear shallow w...

A fractional calculus concept is considered in the framework of a Volterra type integro-differential equation, which employed for self-consistent description high-gain free-electron laser (FEL). It shown that Fox H-function Laplace image kernel also known as FEL equation with Caputo–Fabrizio derivative. Asymptotic solutions are analyzed well.

In this paper, a hybrid technique based on the combining of differential transform approach, Laplace transformation, and Pade approximant is successfully implemented for solving Volterra Integro (VID) equations subject to appropriate conditions. The proposed method known as modified (MDTM) enlarges domain convergence with less computational time. One interesting features algorithm ability produ...

The Tau method, produces approximate polynomial solution of differential, integral and integro-differential equations (see [E.l,Ortiz, The Tau method, SIAM J. Numer. Anal. 6 (3) (1969) 480–492; E.l. Ortiz, H. Samara, An operational approach to the Tau method for the numerical solution of non-linear differential equations, Computing 27 (1981) 15–25; S.M. Hosseini, S. Shahmorad, A matrix formulat...

First, we develop a direct operator method for solving boundary value problems class of nth order linear Volterra–Fredholm integro-differential equations convolution type. The proposed technique is based on the assumption that Volterra bijective and its inverse known in closed form. Existence uniqueness criteria are established exact solution derived. We then apply this to construct form fourth...