Bell wavelets method to solve class of fractional differential equations arising in fluid mechanics

Abstract

This study introduces a new Bell wavelet matrix method to solve a class of fractional differential equations arising in fluid mechanics. The class under consideration comprises the fractional relaxation-oscillation equation (R-OE) as a special case. In this work, the Bell wavelets are constructed using the Bell polynomials and their properties. The fractional operational matrix of integration is developed using block pulse functions (BPFs). The primary benefit of the suggested approach lies in its ability to convert these fractional R-OE into a set of algebraic equations, making them well-suited for computer programming. The present approach’s effectiveness and performance are shown by four test problems. By comparing the solutions obtained through this method with exact solutions and existing methods, we gain insight into the accuracy and reliability of the approach.