Solving Fractional Delay Differential Equations: A New Approach

2015 ◽  
Vol 18 (2) ◽  
Author(s):  
Varsha Daftardar-Gejji ◽  
Yogita Sukale ◽  
Sachin Bhalekar
Keyword(s):  
Differential Equations ◽  
Error Analysis ◽  
Fractional Order ◽  
Delay Differential Equations ◽  
New Method ◽  
New Approach ◽  
Fractional Order Differential Equations ◽  
Fractional Delay ◽  
Delay Differential ◽  
Fractional Delay Differential Equations

AbstractA new method to solve non-linear fractional-order differential equations involving delay has been presented. Applications to a variety of problems demonstrate that the proposed method is more accurate and time efficient compared to existing methods. A detailed error analysis has also been given.

scholarly journals Numerical Study for Time Delay Multistrain Tuberculosis Model of Fractional Order

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Nasser Hassan Sweilam ◽  
Seham Mahyoub Al-Mekhlafi ◽  
Taghreed Abdul Rahman Assiri
Keyword(s):  
Time Delay ◽  
Differential Equations ◽  
Fractional Order ◽  
Delay Differential Equations ◽  
Numerical Study ◽  
Equilibrium Points ◽  
Fractional Delay ◽  
The Stability ◽  
Delay Differential ◽  
Fractional Delay Differential Equations

A novel mathematical fractional model of multistrain tuberculosis with time delay memory is presented. The proposed model is governed by a system of fractional delay differential equations, where the fractional derivative is defined in the sense of the Grünwald–Letinkov definition. Modified parameters are introduced to account for the fractional order. The stability of the equilibrium points is investigated for any time delay. Nonstandard finite deference method is proposed to solve the resulting system of fractional-order delay differential equations. Numerical simulations show that nonstandard finite difference method can be applied to solve such fractional delay differential equations simply and effectively.

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

2021 ◽  
Vol 6 (1) ◽  
pp. 10
Author(s):  
İbrahim Avcı 
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Numerical Solutions ◽  
Fractional Integration ◽  
Operational Matrix ◽  
Absolute Error ◽  
Algebraic Equations ◽  
Fractional Delay ◽  
Delay Differential ◽  
Fractional Delay Differential Equations

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.

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