Abstract
In this work we present a hybrid numerical scheme for the solution of systems of fractional differential equations arising in several fields of engineering. The numerical scheme can deal with both smooth and non-smooth solutions, and, the idea behind the hybrid method is that of approximating the solution as a linear combination of non-polynomial functions in a region near the singularity, and by polynomials in the remaining domain. The numerical method is then used to study fractional RC electrical circuits.
Keywords
- Fractional differential equations
- Caputo derivative
- Non-polynomial collocation method
- Polynomial collocation method
- Electrical circuits
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Acknowledgments
The first, third and fourth authors would like to thank the funding by FCT-Portuguese Foundation for Science and Technology through scholarship and projects: SFRH/BPD/100353/2014 and UID/Multi/04621/2013, UID/MAT/00297/2013 (Centro de Matemática e Aplicações), respectively.
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Ferrás, L.L., Ford, N.J., Morgado, M.L., Rebelo, M. (2019). A Hybrid Numerical Scheme for Fractional-Order Systems. In: Machado, J., Soares, F., Veiga, G. (eds) Innovation, Engineering and Entrepreneurship. HELIX 2018. Lecture Notes in Electrical Engineering, vol 505. Springer, Cham. https://doi.org/10.1007/978-3-319-91334-6_100
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DOI: https://doi.org/10.1007/978-3-319-91334-6_100
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Online ISBN: 978-3-319-91334-6
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