A computational algorithm for the numerical solution of fractional order delay differential equations

•Haar wavelet is developed for the solution of delay fractional order differential equations (FODEs).•The developed technique is applied to both nonlinear and linear delay FODEs.•The derived nonlinear system is solved by Broyden’s technique while the linear system is solved by Gauss elimination tech...

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Vydané v:Applied mathematics and computation Ročník 402; s. 125863
Hlavní autori: Amin, Rohul, Shah, Kamal, Asif, Muhammad, Khan, Imran
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Inc 01.08.2021
Predmet:
Broyden’s technique
Collocation technique
FODEs
Haar wavelet method
Haar wavelet method
Collocation technique
Broyden’s technique
FODEs
ISSN:0096-3003, 1873-5649
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Popis
Shrnutí:•Haar wavelet is developed for the solution of delay fractional order differential equations (FODEs).•The developed technique is applied to both nonlinear and linear delay FODEs.•The derived nonlinear system is solved by Broyden’s technique while the linear system is solved by Gauss elimination technique.•Fractional derivative is described in the Caputo sense throughout the paper. In this paper, a collocation technique based on Haar wavelet is developed for the solution of delay fractional order differential equations (FODEs). The developed technique is applied to both nonlinear and linear delay FODEs. The Haar technique reduces the given equations to a system of nonlinear and linear algebraic equations. The derived nonlinear system is solved by Broyden’s technique while the linear system is solved by Gauss elimination technique. Some examples are taken from literature for checking the validation and convergence of the Haar collocation technique. The comparison of approximate and exact solution are given in figures. The mean square root and maximum absolute errors for distant number of grid points are calculated. The results show that Haar wavelet collocation technique (HWCT) is easy and efficient for solving delay type FODEs. Fractional derivative is described in the Caputo sense throughout the paper.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2020.125863