Abstract In this study, an initial-value problem for a nonlinear Volterra functional integro-differential equation on finite interval was considered. The term in the contains multiple time delays. addition to giving some new theorems existence and uniqueness of solutions equation, authors also prove Hyers-Ulam-Rassias stability Hyers-Ulam equation. proofs use several different tools including B...

Abstract: This article focuses on obtaining analytical solutions for d-dimensional, parabolic Volterra integro-differential equations with different types of frictional memory kernel. Based on Laplace transform and Fourier transform theories, the properties of the Fox-H function and convolution theorem, analytical solutions for the equations in the infinite domain are derived under three fricti...

The paper considers two types of Volterra integral equations the first kind, arising in study inverse problems dynamics controlled heat power systems. main focus work is aimed at studying specifics classes kind that arise when describing nonlinear using apparatus integro-power series. subject area research represented by a simulation model exchange unit element, which describes change enthalpy ...

in this article the nonlinear mixed volterra-fredholm integral equations are investigated by means of the modied three-dimensional block-pulse functions (m3d-bfs). this method converts the nonlinear mixed volterra-fredholm integral equations into a nonlinear system of algebraic equations. the illustrative   examples are provided to demonstrate the applicability and simplicity of our   scheme.

Lyapunov functions/functionals have found their footing in Volterra integro-differential equations. This is not the case for integral equations, and it therefore further explored this paper. In manuscript, we utilize functionals combined with Laplace transform to qualitatively analyze solutions of equation addition, extend our method nonlinear equations infinite delay, several kernels. We menti...

in this paper rationalized haar (rh) functions method is applied to approximate the numerical solution of the fractional volterra integro-differential equations (fvides). the fractional derivatives are described in caputo sense. the properties of rh functions are presented, and the operational matrix of the fractional integration together with the product operational matrix are used to reduce t...

in this paper, we consider an implicit block backwarddifferentiation formula (bbdf) for solving volterraintegro-differential equations (vides). the approach given in thispaper leads to numerical methods for solving vides which avoid theneed for special starting procedures. convergence order and linearstability properties of the methods are analyzed. also, methods withextensive stability region ...