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Computational and Applied Mathematics

, Volume 37, Issue 4, pp 5456–5475 | Cite as

Generalized Jacobi–Galerkin method for nonlinear fractional differential algebraic equations

  • F. Ghanbari
  • K. Ghanbari
  • P. Mokhtary
Article
  • 77 Downloads

Abstract

In this paper, we provide an approximate approach based on the Galerkin method to solve a class of nonlinear fractional differential algebraic equations. The fractional derivative operator in the Caputo sense is utilized and the generalized Jacobi functions are employed as trial functions. The existence and uniqueness theorem as well as the asymptotic behavior of the exact solution are provided. It is shown that some derivatives of the solutions typically have singularity at origin dependence on the order of the fractional derivative. The influence of the perturbed data on the exact solutions along with the convergence analysis of the proposed scheme is also established. Some illustrative examples provided to demonstrate that this novel scheme is computationally efficient and accurate.

Keywords

Fractional differential algebraic equation Generalized Jacobi–Galerkin method Regularity Convergence analysis 

Mathematics Subject Classification

34A09 65L05 65L20 65L60 65L80 

Notes

Acknowledgements

The authors cordially thank anonymous referees for their valuable comments that improved the quality of this paper.

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Basic SciencesSahand University of TechnologyTabrizIran

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