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.