Utilization of Haar wavelet collocation technique for fractal-fractional order problem

This work is devoted for establishing adequate results for the qualitative theory as well as approximate solution of “fractal-fractional order differential equations” (F-FDEs). For the required numerical results, we use Haar wavelet collocation (H-W-C) method which has very rarely utilized for F-FDE...

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Bibliographic Details
Published in:Heliyon 2023-06, Vol.9 (6), p.e17123-e17123, Article e17123
Main Authors: Shah, Kamal, Amin, Rohul, Abdeljawad, Thabet
Format: Article
Language:English
Subjects:
F-FDEs
Fractal-fractional Caputo derivative
H-W-C
Numerical results
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Summary:This work is devoted for establishing adequate results for the qualitative theory as well as approximate solution of “fractal-fractional order differential equations” (F-FDEs). For the required numerical results, we use Haar wavelet collocation (H-W-C) method which has very rarely utilized for F-FDEs. We establish the general algorithm for F-FDEs to compute numerical solution for the considered class. Also, we establish a result devoted to the qualitative theory via Banach fixed point result. A results devoted to Ulam-Hyers (U-H) stability are also included. Two pertinent examples are given along with the comparison and different norms of errors displayed in figures as well as tables.
ISSN:2405-8440
2405-8440
DOI:10.1016/j.heliyon.2023.e17123