A numerical method for fractional variable order pantograph differential equations based on Haar wavelet

In this article, Haar wavelet collocation technique is developed for the solution of variable order fractional pantograph differential equations. The Haar technique reduces the given equations into a system of linear algebraic equations. The derived system is then solved by Gaussian elimination meth...

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Bibliographic Details
Published in:Engineering with computers 2022-06, Vol.38 (3), p.2655-2668
Main Authors: Alrabaiah, Hussam, Ahmad, Israr, Amin, Rohul, Shah, Kamal
Format: Article
Language:English
Subjects:
CAE) and Design
Calculus of Variations and Optimal Control
Optimization
Classical Mechanics
Collocation
Computer Science
Computer-Aided Engineering (CAD
Control
Differential equations
Engineering
Fixed points (mathematics)
Gaussian elimination
Initial conditions
Linear algebra
Math. Applications in Chemistry
Mathematical analysis
Mathematical and Computational Engineering
Mathematical functions
Mathematics
Numerical analysis
Numerical methods
Original Article
Pantographs
Quantum dots
Systems Theory
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Summary:In this article, Haar wavelet collocation technique is developed for the solution of variable order fractional pantograph differential equations. The Haar technique reduces the given equations into a system of linear algebraic equations. The derived system is then solved by Gaussian elimination method. Through fixed point theory, we develop some requisite conditions for the existence of at most one solution of the underlying problem endowed with initial conditions. Some numerical examples are also given for checking the validation and convergence of the concerned method. The mean square root and maximum absolute errors for different number of collocation points have been calculated. The results indicate that Haar method is efficient for solving such equations. Fractional derivative is described in the Caputo sense.
ISSN:0177-0667
1435-5663
DOI:10.1007/s00366-020-01227-0