A numerical method based on finite difference for solving fractional delay differential equations

TL;DR: A family of piecewise functions is proposed, based on which the fractional order integration of the Müntz-Legendre wavelets are easy to calculate, and this operational matrix with the collocation points is used to reduce the under study problem to a system of algebraic equations.

TL;DR: In this article, a neural network based approach was proposed to approximate the solution of fractional delay differential equations with delay using a new approach based on artificial neural networks, and the neural network effectiveness and applicability were validated by solving different types of fractiona-delay differential equations, linear systems with delay, nonlinear systems with delays, and a system of differential equations.

TL;DR: In this article, the authors numerically simulate the results of fractional delay differential equations (DDEs) using chebyshev polynomials and compare the results with some existing solutions.

TL;DR: The shifted Jacobi polynomial scheme is used to solve the results by deriving operational matrix for the fractional differentiation and integration in the Caputo and Riemann–Liouville sense, respectively.

TL;DR: In this paper, Liapunov functional for autonomous systems is used to define the saddle point property near equilibrium and periodic orbits for linear systems, which is a generalization of the notion of stable D operators.

TL;DR: Delay Differential Equations as mentioned in this paper are a generalization of delay differential equations and have been used in a variety of applications in population dynamics, such as global stability for single species models and multi-species models.

TL;DR: In this paper, the authors introduce the study of differential difference equations and discuss some of the main features of the theory, and discuss the asymptotic behavior of solutions and the problem of stability.

TL;DR: In this paper, the authors present an overview of state estimates of stochastic systems with delay and their control for deterministic FEDs, including optimal control of Stochastic Delay Systems.