Application of fractional calculus to the electroviscoelastic behaviour of liquid/liquid interfaces
Abstract
Using fractional-order alpha (0,1) , capacitive and inductive elements one can obtain linear
and/or nonlinear fractional integral-differential equation of the van der Pol type, i.e. more
generalized mathematical formalism for description of the electroviscoelastic behavior of
liquid/liquid interfaces e.g. in finely dispersed systems, emulsions or double emulsions. First,
in this paper, it is obtained nonlinear van der Pol model applying (alpha,beta ) order and variable
order approach, alpha =alpha (t) . Also,it is proposed applying generalized differential transform
method using Caputo definition of fractional operators to obtain a analytical homogeneous
solution of a linear equation of van der Pol model of non-integer order. Finally, it is proposed
numerical algorithm using approximation of Caputo derivative for calculating the corresponding
homogeneous solution of linear fractional differential equation of the van der Pol type.
Keywords:
fractional calculus / electroviscoelastic / liquid/liquid interfaces / van der Pol typeSource:
Proceedings of 18th International Congress of Chemical and Process Engineering 24th - 28th August 2008, Prague - Czech Republic, 2008, 1-9Publisher:
- Prague: Czech society of chemical engineering
Funding / projects:
- Fini disperzni sistemi: mikro-, nano-, ato-inženjerstvo (RS-MESTD-MPN2006-2010-142034)
Collections
Institution/Community
Mašinski fakultetTY - CONF AU - Lazarević, Mihailo AU - Spasić, Aleksandar AU - Bučanović, Ljubiša AU - Krstić, Dimitrije PY - 2008 UR - https://machinery.mas.bg.ac.rs/handle/123456789/5183 AB - Using fractional-order alpha (0,1) , capacitive and inductive elements one can obtain linear and/or nonlinear fractional integral-differential equation of the van der Pol type, i.e. more generalized mathematical formalism for description of the electroviscoelastic behavior of liquid/liquid interfaces e.g. in finely dispersed systems, emulsions or double emulsions. First, in this paper, it is obtained nonlinear van der Pol model applying (alpha,beta ) order and variable order approach, alpha =alpha (t) . Also,it is proposed applying generalized differential transform method using Caputo definition of fractional operators to obtain a analytical homogeneous solution of a linear equation of van der Pol model of non-integer order. Finally, it is proposed numerical algorithm using approximation of Caputo derivative for calculating the corresponding homogeneous solution of linear fractional differential equation of the van der Pol type. PB - Prague: Czech society of chemical engineering C3 - Proceedings of 18th International Congress of Chemical and Process Engineering 24th - 28th August 2008, Prague - Czech Republic T1 - Application of fractional calculus to the electroviscoelastic behaviour of liquid/liquid interfaces EP - 9 SP - 1 UR - https://hdl.handle.net/21.15107/rcub_machinery_5183 ER -
@conference{ author = "Lazarević, Mihailo and Spasić, Aleksandar and Bučanović, Ljubiša and Krstić, Dimitrije", year = "2008", abstract = "Using fractional-order alpha (0,1) , capacitive and inductive elements one can obtain linear and/or nonlinear fractional integral-differential equation of the van der Pol type, i.e. more generalized mathematical formalism for description of the electroviscoelastic behavior of liquid/liquid interfaces e.g. in finely dispersed systems, emulsions or double emulsions. First, in this paper, it is obtained nonlinear van der Pol model applying (alpha,beta ) order and variable order approach, alpha =alpha (t) . Also,it is proposed applying generalized differential transform method using Caputo definition of fractional operators to obtain a analytical homogeneous solution of a linear equation of van der Pol model of non-integer order. Finally, it is proposed numerical algorithm using approximation of Caputo derivative for calculating the corresponding homogeneous solution of linear fractional differential equation of the van der Pol type.", publisher = "Prague: Czech society of chemical engineering", journal = "Proceedings of 18th International Congress of Chemical and Process Engineering 24th - 28th August 2008, Prague - Czech Republic", title = "Application of fractional calculus to the electroviscoelastic behaviour of liquid/liquid interfaces", pages = "9-1", url = "https://hdl.handle.net/21.15107/rcub_machinery_5183" }
Lazarević, M., Spasić, A., Bučanović, L.,& Krstić, D.. (2008). Application of fractional calculus to the electroviscoelastic behaviour of liquid/liquid interfaces. in Proceedings of 18th International Congress of Chemical and Process Engineering 24th - 28th August 2008, Prague - Czech Republic Prague: Czech society of chemical engineering., 1-9. https://hdl.handle.net/21.15107/rcub_machinery_5183
Lazarević M, Spasić A, Bučanović L, Krstić D. Application of fractional calculus to the electroviscoelastic behaviour of liquid/liquid interfaces. in Proceedings of 18th International Congress of Chemical and Process Engineering 24th - 28th August 2008, Prague - Czech Republic. 2008;:1-9. https://hdl.handle.net/21.15107/rcub_machinery_5183 .
Lazarević, Mihailo, Spasić, Aleksandar, Bučanović, Ljubiša, Krstić, Dimitrije, "Application of fractional calculus to the electroviscoelastic behaviour of liquid/liquid interfaces" in Proceedings of 18th International Congress of Chemical and Process Engineering 24th - 28th August 2008, Prague - Czech Republic (2008):1-9, https://hdl.handle.net/21.15107/rcub_machinery_5183 .