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

Date

2021

Authors

Chouhan, Devendra
Mishra, Vinod
Srivastava, H.M.

Journal Title

Journal ISSN

Volume Title

Publisher

Results in Applied Mathematics

Abstract

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.

Description

Keywords

Generalized fractional-order Bernoulli wavelets, Variable order fractional differential equations, Operational matrix, Liouville-Caputo fractional derivative

Citation

Chouhan, D., Mishra, V., & Srivastava, H. M. (2021). Bernoulli wavelet method for numerical solution of anomalous infiltration and diffusion modeling by nonlinear fractional differential equations of variable order. Results in Applied Mathematics, 10, 1-13. https://doi.org/10.1016/j.rinam.2021.100146.