Utilization of Haar wavelet collocation technique for fractal-fractional order problem
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Published on: August 30, 2013
Kamal Shah1,2, Rohul Amin3, Thabet Abdeljawad1,4
1Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia.
Abstract:
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.
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