Sumudu Decomposition Method for Solving Fractional Delay Differential Equations

Decomposition Method ◽

Integral Transform ◽

Adomian Decomposition Method ◽

Approximate Solutions ◽

Adomian Decomposition ◽

Fractional Delay ◽

Delay Differential ◽

The idea of the paper is to consolidate Mahgoub transform and variational iteration method (MTVIM) to solve fractional delay differential equations (FDDEs). The fractional derivative was in Caputo sense. The convergences of approximate solutions to exact solution were quick. The MTVIM is characterized by ease of application in various problems and is capable of simplifying the size of computational operations. Several non-linear (FDDEs) were analytically solved as illustrative examples and the results were compared numerically. The results for accentuating the efficiency, performance, and activity of suggested method were shown by comparisons with Adomian Decomposition Method (ADM), Laplace Adomian Decomposition Method (LADM), Modified Adomian Decomposition Method (MADM) and Homotopy Analysis Method (HAM).

Representation of solutions of nonhomogeneous conformable fractional delay differential equations

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2021.111190 ◽

2021 ◽

Vol 150 ◽

pp. 111190

Author(s):

Nazim I. Mahmudov ◽

Mustafa Aydın

Keyword(s):

Differential Equations ◽

Representation Of Solutions ◽

Fractional Delay ◽

Delay Differential ◽

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

Journal of Taibah University for Science ◽

10.1016/j.jtusci.2013.07.002 ◽

2013 ◽

Vol 7 (3) ◽

pp. 120-127 ◽

Cited By ~ 34

Author(s):

Behrouz P. Moghaddam ◽

Zeynab S. Mostaghim

Keyword(s):

Finite Difference ◽

Differential Equations ◽

Numerical Method ◽

Fractional Delay ◽

Delay Differential ◽

Existence of positive solutions of nonlinear fractional delay differential equations

Positivity ◽

10.1007/s11117-008-2251-6 ◽

2008 ◽

Vol 13 (3) ◽

pp. 601-609 ◽

Cited By ~ 17

Author(s):

Chunping Liao ◽

Haiping Ye

Keyword(s):

Differential Equations ◽

Positive Solutions ◽

Existence Of Positive Solutions ◽

Fractional Delay ◽

Delay Differential ◽

Numerical Simulation of Fractional Delay Differential Equations Using the Operational Matrix of Fractional Integration for Fractional-Order Taylor Basis

Fractal and Fractional ◽

10.3390/fractalfract6010010 ◽

2021 ◽

Vol 6 (1) ◽

pp. 10

Author(s):

İbrahim Avcı

Keyword(s):

Differential Equations ◽

Numerical Solutions ◽

Fractional Integration ◽

Operational Matrix ◽

Absolute Error ◽

Algebraic Equations ◽

Fractional Delay ◽

Delay Differential ◽

In this paper, we consider numerical solutions for a general form of fractional delay differential equations (FDDEs) with fractional derivatives defined in the Caputo sense. A fractional integration operational matrix, created using a fractional Taylor basis, is applied to solve these FDDEs. The main characteristic of this approach is, by utilizing the operational matrix of fractional integration, to reduce the given differential equation to a set of algebraic equations with unknown coefficients. This equation system can be solved efficiently using a computer algorithm. A bound on the error for the best approximation and fractional integration are also given. Several examples are given to illustrate the validity and applicability of the technique. The efficiency of the presented method is revealed by comparing results with some existing solutions, the findings of some other approaches from the literature and by plotting absolute error figures.

Monotone Iteration Principle in the Theory of Hadamard Fractional Delay Differential Equations

Current Developments in Mathematical Sciences - Frontiers in Fractional Calculus ◽

10.2174/9781681085999118010008 ◽

2018 ◽

pp. 132-158

Author(s):

Kishor D. Kucche

Keyword(s):

Differential Equations ◽

Monotone Iteration ◽

Fractional Delay ◽

Delay Differential ◽

On the convergence of Jacobi‐Gauss collocation method for linear fractional delay differential equations

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.6934 ◽

2020 ◽

Vol 44 (2) ◽

pp. 2237-2253

Author(s):

N. Peykrayegan ◽

M. Ghovatmand ◽

M. H. Noori Skandari

Keyword(s):

Differential Equations ◽

Collocation Method ◽

Fractional Delay ◽

Delay Differential ◽

Generalized Adams method for solving fractional delay differential equations

Mathematics and Computers in Simulation ◽

10.1016/j.matcom.2020.09.006 ◽

2021 ◽

Vol 180 ◽

pp. 401-419

Author(s):

Jingjun Zhao ◽

Xingzhou Jiang ◽

Yang Xu

Keyword(s):

Differential Equations ◽

Adams Method ◽

Fractional Delay ◽

Delay Differential ◽

Dependence Analysis of the Solutions on the Parameters of Fractional Delay Differential Equations

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.10-m1045 ◽

2011 ◽

Vol 3 (5) ◽

pp. 586-597 ◽

Cited By ~ 3

Author(s):

Shuiping Yang ◽

Aiguo Xiao ◽

Xinyuan Pan

Keyword(s):

Differential Equations ◽

Initial Function ◽

Hand Function ◽

Dependence Analysis ◽

Numerical Examples ◽

Fractional Delay ◽

Delay Differential ◽

Fractional Delay Differential Equations ◽

Theoretical Results

AbstractIn this paper, we investigate the dependence of the solutions on the parameters (order, initial function, right-hand function) of fractional delay differential equations (FDDEs) with the Caputo fractional derivative. Some results including an estimate of the solutions of FDDEs are given respectively. Theoretical results are verified by some numerical examples.

An Extended Predictor–Corrector Algorithm for Variable-Order Fractional Delay Differential Equations

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4032574 ◽

2016 ◽

Vol 11 (6) ◽

Cited By ~ 36

Author(s):

B. Parsa Moghaddam ◽

Sh. Yaghoobi ◽

J. A. Tenreiro Machado

Keyword(s):

Differential Equations ◽

Fractional Derivatives ◽

Variable Order ◽

The Novel ◽

Fractional Delay ◽

Novel Method ◽

Delay Differential ◽

Predictor Corrector ◽

This article presents a numerical method based on the Adams–Bashforth–Moulton scheme to solve variable-order fractional delay differential equations (VFDDEs). In these equations, the variable-order (VO) fractional derivatives are described in the Caputo sense. The existence and uniqueness of the solutions are proved under Lipschitz condition. Numerical examples are presented showing the applicability and efficiency of the novel method.