A Numerical Technique Based on Bernoulli Wavelet Operational Matrices for Solving a Class of Fractional Order Differential Equations

Abstract

In this paper, we present an efficient, new, and simple programmable method for finding approximate solutions to fractional differential equations based on Bernoulli wavelet approximations. Bernoulli Wavelet functions involve advantages such as orthogonality, simplicity, and ease of usage, in addition to the fact that fractional Bernoulli wavelets have exact operational matrices that improve the accuracy of the applied approach. A fractional differential equation was simplified to a system of algebraic equations using the fractional order integration operational matrices of Bernoulli wavelets. Examples are used to demonstrate the technique’s precision.

Keywords

• Bernoulli wavelets
• fractional differential equations
• Caputo derivative
• fractional integration operational Bernoulli wavelet matrix
• numerical solution