Mathematical analysis

Ecology

Simulation

Delay differential equation

Artificial intelligence

Singularity

Economics

Physics

Nonlinear system

Finance

Mathematics

Biology

Quantum mechanics

Order (exchange)

Computer science

Differential equation

Algorithm

Correctness

Type (biology)

Applied mathematics

Computer simulation

Artificial neural network

Differential (mechanical device)

Thermodynamics

Mathematical Problems in Engineering

In this study, the design of a novel model based on nonlinear third-order Emden–Fowler delay differential (EF-DD) equations is presented along with two types using the sense of delay differential and standard form of the second-order EF equation. The singularity at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>ξ</mml:mi></mml:math> = 0 at single or multiple points of each type of the designed EF-DD model are discussed. The detail of shape factors and delayed points is provided for both types of the designed third-order EF-DD model. For the verification and validation of the model, two numerical examples are presented of each case and numerical results have been performed using the artificial neural network along with the hybrid of global and local capabilities. The comparison of the obtained numerical results with the exact solutions shows the perfection and correctness of the designed third-order EF-DD model.

Design and Numerical Solutions of a Novel Third-Order Nonlinear Emden–Fowler Delay Differential Model