This paper focuses on the fuzzy Volterra integro-differential equation of nth order of the second-kind with nonlinear fuzzy kernel and initial values. The derived integral equations are solvable, the solutions of which are unique under certain conditions. The existence and uniqueness of the solutions are investigated in a theorem and an upper boundary is found for solutions. Comparison of the e...

here a posteriori error estimate for the numerical solution of nonlinear voltena- hammerstein equations is given. we present an error upper bound for nonlinear voltena-hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of brunner for these problems (the implicitly linear collocation method).we al...

This article introduces a numerical method based on an M(n+ 1) set of general, hybrid orthonormal Bernstein functions coupled with Block-Pulse Functions(HOBB) on the interval [0,1] for approximating solutions of a Coupled System of linear and non linear Volterra integral and Integro-Differential equations. This method reduces a Coupled System of Volterra integral and IntegroDifferential equatio...

We survey continuous and discrete regularization methods for first-kind Volterra problems with continuous kernels. Classical regularization methods tend to destroy the non-anticipatory (or causal) nature of the original Volterra problem because such methods typically rely on computation of the Volterra adjoint operator, an anticipatory operator. In this survey we pay special attention to partic...

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...

We apply the Radu–Miheţ method derived from an alternative fixed-point theorem with a class of matrix-valued fuzzy controllers to approximate fractional Volterra integro-differential equation ψ-Hilfer derivative in k-normed spaces obtain approximation for this type equation.

This paper applies He’s variational iteration method for solving two systems of Volterra integro-differential equations. The solution process is illustrated and various physically relevant results are obtained. Comparison of the obtained results with exact solutions shows that the used method is an effective and highly promising method for various classes of both linear and nonlinear integro-di...

Email: [email protected] Abstract: In this study, we contribute to the existing theory of abstract degenerate Volterra integro-differential equations in sequentially complete locally convex spaces. We investigate a class of abstract degenerate Volterra inclusions by using the multivalued linear operator approach, as well as a class of abstract degenerate multi-term fractional differential equat...

Abstract. In this paper, a method is employed to approximate the solution of two-dimensional nonlinear Volterra integro-differential equations (2DNVIDEs) with supplementary conditions. First, we introduce twodimensional Legendre polynomials, then convert 2DNVIDEs to the two-dimensional linear Volterra integrodifferential equations (2DLVIDEs). Using this properties and collocation points, reduce...