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Galerkin finite element method for nonlinear fractional differential equations.
- Source :
-
Numerical Algorithms . Sep2021, Vol. 88 Issue 1, p113-141. 29p. - Publication Year :
- 2021
-
Abstract
- In this paper, we study the existence, regularity, and approximation of the solution for a class of nonlinear fractional differential equations. In order to do this, suitable variational formulations are defined for nonlinear boundary value problems with Riemann-Liouville and Caputo fractional derivatives together with the homogeneous Dirichlet condition. We investigate the well-posedness and also the regularity of the corresponding weak solutions. Then, we develop a Galerkin finite element approach for the numerical approximation of the weak formulations and drive a priori error estimates and prove the stability of the schemes. Finally, some numerical experiments are provided to demonstrate the accuracy of the proposed method. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10171398
- Volume :
- 88
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Numerical Algorithms
- Publication Type :
- Academic Journal
- Accession number :
- 151818921
- Full Text :
- https://doi.org/10.1007/s11075-020-01032-2