Razumikhin qualitative analyses of Volterra integro-fractional delay differential equation with caputo derivatives

2021 ◽  
Vol 103 ◽  
pp. 106037 ◽  
Author(s):  
John R. Graef ◽  
Cemil Tunç ◽  
Hamdullah Şevli
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Caputo Derivatives ◽  
Fractional Delay ◽  
Delay Differential ◽  
Qualitative Analyses

scholarly journals A Specific Method for Solving Fractional Delay Differential Equation via Fraction Taylor’s Series

2022 ◽  
Vol 2022 ◽  
pp. 1-6
Author(s):  
Ming-Jing Du
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Approximate Solutions ◽  
Specific Method ◽  
Fractional Taylor’S Series ◽  
Fractional Delay ◽  
Delay Differential ◽  
Taylor’S Series

It is well known that the appearance of the delay in the fractional delay differential equation (FDDE) makes the convergence analysis very difficult. Dealing with the problem with the traditional reproducing kernel method (RKM) is very tricky. The feature of this paper is to gain a more credible approximate solution via fractional Taylor’s series (FTS). We use the FTS to deal with the delay for improving the accuracy of the approximate solutions. Compared with other methods, the five numerical examples demonstrate the accuracy and efficiency of the proposed method in this paper.

scholarly journals An Approximation Technique for Fractional Order Delay Differential Equations

2019 ◽  
pp. 1539-1545
Author(s):  
Olutunde Samuel Odetunde ◽  
Abass Ishola Taiwo ◽  
Olusola Adebanwo Dehinsilu
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Decomposition Method ◽  
Convergent Series ◽  
Approximation Technique ◽  
Test Problems ◽  
Research Article ◽  
Iterative Decomposition ◽  
Fractional Delay ◽  
Delay Differential

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.

scholarly journals Hermite Wavelet Method for Fractional Delay Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Umer Saeed ◽  
Mujeeb ur Rehman
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Wavelet Method ◽  
Numerical Examples ◽  
Method Of Steps ◽  
Fractional Delay ◽  
Delay Differential ◽  
Fractional Delay Differential Equations

We proposed a method by utilizing method of steps and Hermite wavelet method, for solving the fractional delay differential equations. This technique first converts the fractional delay differential equation to a fractional nondelay differential equation and then applies the Hermite wavelet method on the obtained fractional nondelay differential equation to find the solution. Several numerical examples are solved to show the applicability of the proposed method.

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