A Hybrid Numerical Scheme for Fractional-Order Systems
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.
KeywordsFractional differential equations Caputo derivative Non-polynomial collocation method Polynomial collocation method Electrical circuits
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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