Bernoulli wavelet method for numerical solution of anomalous infiltration and diffusion modeling by nonlinear fractional differential equations of variable order

In this paper, generalized fractional-order Bernoulli wavelet functions based on the Bernoulli wavelets are constructed to obtain the numerical solution of problems of anomalous infiltration and diffusion modeling by a class of nonlinear fractional differential equations with variable order. The idea is to use Bernoulli wavelet functions and operational matrices of integration. Firstly, the generalized fractional-order Bernoulli wavelets are constructed. Secondly, operational matrices of integration are derived and utilize to convert the fractional differential equations (FDE) into a system of algebraic equations. Finally, some numerical examples are presented to demonstrate the validity, applicability and accuracy of the proposed Bernoulli wavelet method. (C) 2021 The Authors. Published by Elsevier B.V.

Automated summary

This paper introduces a generalized fractional-order Bernoulli wavelet function based on Bernoulli wavelets to solve problems of variable-order nonlinear fractional differential equations. By constructing wavelet functions and using operational matrices of integration, the fractional differential equations are converted into algebraic equations. Numerical examples are provided to demonstrate the effectiveness, applicability, and accuracy of the proposed Bernoulli wavelet method.