Haar wavelet based numerical technique for the solutions of fractional advection diffusion equations
S.G. Ahmed, Shah Jahan, Kottakkaran Sooppy Nisar
Abstract
In this article, a new numerical technique based on Haar wavelet is introduced to solve the time fractional advection diffusion equations (TFADEs). First we have constructed a generalized operational matrix of fractional order integration using Haar wavelet without taking block pulse functions into account. The fractional derivative in these problems is in the Caputo sense. In the proposed technique, the unknown function is approximated by truncated Haar wavelet series. The efficiency of the computational approach is examined and validated using particular test problems, and are compared with those of existing methodologies. The numerical results show that the proposed technique is computationally more efficient and yields high accuracy over those methodologies. The behaviour of solutions of fractional order \(\alpha\) and their graphical representation is shown by using MATLAB (R2022a) at various values.