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Generalized Jacobi–Galerkin method for nonlinear fractional differential algebraic equations

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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.

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Acknowledgements

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

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran

    F. Ghanbari, K. Ghanbari & P. Mokhtary

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  1. F. Ghanbari
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  2. K. Ghanbari
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  3. P. Mokhtary
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Correspondence to P. Mokhtary.

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Communicated by Vasily E. Tarasov.

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Ghanbari, F., Ghanbari, K. & Mokhtary, P. Generalized Jacobi–Galerkin method for nonlinear fractional differential algebraic equations. Comp. Appl. Math. 37, 5456–5475 (2018). https://doi.org/10.1007/s40314-018-0645-z

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