An Approximation Technique for Fractional Order Delay Differential Equations

Olutunde Samuel Odetunde,Olusola Adebanwo Dehinsilu,Abass Ishola Taiwo

doi:10.24996/ijs.2019.60.7.14

Olutunde Samuel Odetunde, Olusola Adebanwo Dehinsilu + Show 1 more

Open Access

https://doi.org/10.24996/ijs.2019.60.7.14

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Abstract

In this research article, an Iterative Decomposition Method is applied to approximate linear and non-linear fractional delay differential equation. The method was used to express the solution of a Fractional delay differential equation in the form of a convergent series of infinite terms which can be effortlessly computable.The method requires neither discretization nor linearization. Solutions obtained for some test problems using the proposed method were compared with those obtained from some methods and the exact solutions. The outcomes showed the proposed approach is more efficient and correct.

Highlights

Fractional Differential Equations (FDE), that are a generalization of the differential equation were applied to model many physical phenomena very appropriately [1]
Fractional Delay Differential equations (FDDE) are current, there exist a variety of materials in the literature, as an example, [4] described the situations for the existence of the solution of Fractional Delay Differential Equations with Riemann- Liouinlle derivatives
In [5, 6], the existence of positive solution for a class of single – term Fractional Delay Differential Equations are taken into consideration, whilst [6 – 9] considered the steadiness of Fractional Delay Differential Equation

Summary

Introduction

Fractional Differential Equations (FDE), that are a generalization of the differential equation were applied to model many physical phenomena very appropriately [1]. In this research article, Fractional Delay Differential equation of the form y(. Several authors have taken into consideration the approximation of Delay Differential Equations of integer order and these consist of the researches of [10 – 14] even as [15 – 16] taken into consideration the method of splines. Applied a combination of the trapezoidal and Simpson rule to find a series solution of FDDEs, while [21] implemented the Chebyshev Wavelet approach. Decomposition Method which has been carried out effectively for integer order differential equations consisting of Delay Differential Equations [18]. The method is devoid of any form of linearization or discretization [1]

Materials and Methods

Results and Discussion

Conclusion