Although perturbation techniques are widely applied to analyze nonlinear problems in science and engineering, they are however so strongly dependent on small parameters appeared in equations under consideration that they are restricted only to weakly nonlinear problems. For strongly nonlinear problems which don’t contain any small parameters, perturbation techniques are invalid. So, it seems ne...

For scientists conducting research, fractional integral differential equation analysis is crucial. Therefore, in this study, we investigate utilizing a novel method called the decomposition method, which applicable to nonlinear Fredholm integro-differential equations. Then, apply approach five test problems for general derivative [Formula: see text] involving To best of our knowledge, are first...

This paper presents a ε-uniform and reliable numerical scheme to solve second-order singularly perturbed Volterra–Fredholm integro-differential equations. Some properties of the analytical solution are given, finite difference is established on non-uniform mesh by using interpolating quadrature rules linear basis functions. An error analysis successfully carried out Boglaev–Bakhvalov-type mesh....

A novel and effective method based on Haar wavelets and Block Pulse Functions (BPFs) is proposed to solve nonlinear Fredholm integro-differential equations of fractional order. The operational matrix of Haar wavelets via BPFs is derived and together with Haar wavelet operational matrix of fractional integration are used to transform the mentioned equation to a system of algebraic equations. Our...