Chouhan, DevendraMishra, VinodSrivastava, H.M.2021-03-012021-03-0120212021Chouhan, 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.https://doi.org/10.1016/j.rinam.2021.100146http://hdl.handle.net/1828/12730In 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.enGeneralized fractional-order Bernoulli waveletsVariable order fractional differential equationsOperational matrixLiouville-Caputo fractional derivativeArticle