2019/09/18 by Nedaiasl, Khadijeh, Dehbozorgi, Raziyeh
#26A33 #65J15 #65L60 #65R20 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.1909.08295
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 a 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 \colorbluefor 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.