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

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.

Keywords

• Fractal-fractional Caputo derivative
• H-W-C
• F-FDEs
• Numerical results