The main aim presented in this article is to provide an efficient transferred Legendre
pseudospectral method for solving pantograph delay differential equations. At the first step …

Delay Ordinary and Partial Differential Equations is devoted to linear and nonlinear ordinary
and partial differential equations with constant and variable delay. It considers qualitative …

This paper is concerned with the application of the spectral tau and collocation methods to
delay multi-order fractional differential equations with vanishing delay rx (0< r< 1). The …

This paper proposes a new approach using the collocation technique for the numerical
solution of a class of second-order Emden–Fowler pantograph differential equations. In the …

We study nonlinear pantograph-type reaction–diffusion PDEs, which, in addition to the
unknown u= u (x, t), also contain the same functions with dilated or contracted arguments of …

We present an efficient numerical method for solving fractional pantograph differential
equations by applying Taylor wavelets. We give an exact formula for the Riemann-Liouville …

The present study aims to design a mathematical system based on the Lane–Emden third‐
order pantograph differential model by using the general forms of the pantograph as well as …

The manuscript is concerned with a generalization of the fractional pantograph equation
which contains a linear functional argument. This type of equation has applications in many …

We present a neuro-heuristic computing platform for finding the solution for initial value
problems (IVPs) of nonlinear pantograph systems based on functional differential equations …

The delay differential equations are of great importance in real-life phenomena. A special
type of these equations is the Pantograph delay differential equation. Generally, solving a …