Fractional calculus, which deals with the concept of fractional derivatives and integrals, has become an important area research, due to its ability capture memory effects non-local behavior in modeling real-world phenomena. In this work, we study a new class Volterra–Fredholm integro-differential equations, involving Caputo–Katugampola derivative. By applying Krasnoselskii Banach fixed-point t...

In this paper, we propose a method to approximate the solution of a linear Fredholm integro-differential equation by using the Chebyshev wavelet of the first kind as basis. For this purpose, we introduce the first Chebyshev operational matrix of integration. Chebyshev wavelet approximating method is then utilized to reduce the integro-differential equation to a system of algebraic equations. Il...

Solution of some practical problems is reduced to the solution of the integro-differential equations. But for the numerical solution of such equations basically quadrature methods or its combination with multistep or one-step methods are used. The quadrature methods basically is applied to calculation of the integral participating in right hand side of integro-differential equations. As this in...

In this study, a Taylor method is developed for numerically solving the high-order most general nonlinear Fredholm integro-differential-difference equations in terms of Taylor expansions. The method is based on transferring the equation and conditions into the matrix equations which leads to solve a system of nonlinear algebraic equations with the unknown Taylor coefficients. Also, we test the ...

Abstract This paper presents an appropriate numerical method to solve nonlinear Fredholm integro-differential equations with time delay. Its approach is based on the Taylor expansion. This method converts the integro-differential equation and the given conditions into the matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Taylor expansion coefficients, s...

s of PhD Theses at Irish Universities 2007 On the Asymptotic Behaviour of Deterministic and Stochastic Volterra Integro–Differential Equations