In this paper, we study a Volterra–Fredholm integro-differential equation. The considered problem involves the fractional Caputo derivatives under some conditions on order. We prove an existence and uniqueness analytic result by application of Banach principle. Then, another that deals with at least one solution is delivered, sufficient for are established means fixed point theorem Schaefer. Ul...

Abstract In this paper, a nonclassical sinc collocation method is constructed for the numerical solution of systems second-order integro-differential equations Volterra and Fredholm types. The novelty approach based on using new weight function instead classic ones. functions used to reduce system algebraic equations. Furthermore, convergence proposed theoretically, showing that converges expon...

This paper appertains the presentation of a Clenshaw–Curtis rule to evaluate highly oscillatory Fredholm integro-differential equations (FIDEs) with Cauchy and weak singularities. To calculate singular integral, unknown function approximated by an interpolation polynomial is rewritten as Taylor series expansion. A system linear FIDEs obtained using equally spaced points collocation solved obtai...

This study introduced new technique which is based on a combination of the least-squares (LST) with Chebyshev and Legendre polynomials for finding approximate solutions higher-order linear Fredholm-Volterra integro-differential equations (FVIDEs) subject to mixed conditions. Two examples second third-order FVIDEs are considered illustrate proposed method, numerical results comprised demonstrate...

In this paper, a useful matrix approach for high-order linear Fredholm integro-differential equations with initial boundary conditions expressed as Lucas polynomials is proposed. Using equationwhich equivalent to set of algebraic the method transforms equation. When compared other methods that have been proposed in literature, numerical results from suggested technique reveal it effective and p...

In this paper, we propose a different way for solving systems of nonlinear Fredholm integral equations the second kind. We construct our new strategy in two steps, through beginning with linearization phase system by applying Newton method, then pass to discretization some involved operator using Nystr\"{o}m method. The convergence analysis method is proved under necessary conditions. At last, ...