Results concerning to approximate controllability of non‐densely defined Sobolev‐type Hilfer fractional neutral delay differential system

2021 ◽  
Author(s):  
Kottakkaran Sooppy Nisar ◽  
V. Vijayakumar
Keyword(s):  
Differential System ◽  
Approximate Controllability ◽  
Sobolev Type ◽  
Neutral Delay ◽  
Delay Differential System ◽  
Delay Differential ◽  
Densely Defined

scholarly journals Applications of Legendre spectral collocation method for solving system of time delay differential equations

2020 ◽  
Vol 12 (6) ◽  
pp. 168781402092211
Author(s):  
Sami Ullah Khan ◽  
Ishtiaq Ali
Keyword(s):  
Time Delay ◽  
Differential Equations ◽  
Collocation Method ◽  
Differential System ◽  
Numerical Test ◽  
Spectral Collocation Method ◽  
Numerical Techniques ◽  
Spectral Collocation ◽  
Delay Differential System ◽  
Delay Differential

The numerical techniques are regarded as the backbone of modern research. In literature, the exact solution of time delay differential models are hardly achievable or impossible. Therefore, numerical techniques are the only way to find their solution. In this article, a novel numerical technique known as Legendre spectral collocation method is used for the approximate solution of time delay differential system. Legendre spectral collocation method and their properties are applied to determined the general procedure for solving time delay differential system with detail error and convergence analysis. The method first convert the proposed system to a system of ordinary differential equations and then apply the Legendre polynomials to solve the resultant system efficiently. Finally, some numerical test problems are given to confirm the efficiency of the method and were compared with other available numerical schemes in the literature.

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