{"title":"Application of a SubIval Numerical Solver for Fractional Circuits","authors":"Marcin Sowa","volume":140,"journal":"International Journal of Electrical and Computer Engineering","pagesStart":546,"pagesEnd":551,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10009391","abstract":"The paper discusses the subinterval-based numerical
\r\nmethod for fractional derivative computations. It is now referred
\r\nto by its acronym – SubIval. The basis of the method is briefly
\r\nrecalled. The ability of the method to be applied in time stepping
\r\nsolvers is discussed. The possibility of implementing a time step size
\r\nadaptive solver is also mentioned. The solver is tested on a transient
\r\ncircuit example. In order to display the accuracy of the solver –
\r\nthe results have been compared with those obtained by means of a
\r\nsemi-analytical method called gcdAlpha. The time step size adaptive
\r\nsolver applying SubIval has been proven to be very accurate as
\r\nthe results are very close to the referential solution. The solver is
\r\ncurrently able to solve FDE (fractional differential equations) with
\r\nvarious derivative orders for each equation and any type of source
\r\ntime functions.","references":"[1] K.B. Oldham, J. Spanier, The Fractional Calculus, Academic Press, New\r\nYork (1974).\r\n[2] P.W. Ostalczyk, P. Duch, D.W. Brzezi\u00b4nski, D. Sankowski, \u201dOrder\r\nFunctions Selection in the Variable-, Fractional-Order PID Controller\u201d,\r\nAdvances in Modelling and Control of Non-integer-Order Systems,\r\nSpringer, 159\u2013170 (2015).\r\n[3] D. Spa\u0142ek, \u201dSynchronous Generator Model with Fractional Order\r\nVoltage Regulator PIbDa\u201d, Acta Energetica 2\/23, 78\u201384 (2015).\r\n[4] L. Mescia, P. Bia, D. Caratelli, \u201dFractional Derivative Based FDTD\r\nModeling of Transient Wave Propagation in Havriliak-Negami media\u201d,\r\nIEEE Transactions on Microwave Theory and Techniques 62 (9),\r\n1920\u20131929 (2014).\r\n[5] R. Garrappa, G. 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