Fractional order Van der Pol model of electroviscoelasticity of liquid/liquid interfaces: analytical and numerical solution
Само за регистроване кориснике
2009
Конференцијски прилог (Објављена верзија)
Метаподаци
Приказ свих података о документуАпстракт
A new, recently developed, theory of electroviscoelasticity describes the behavior of electrified liquid-liquid interfaces in fine dispersed systems, and is based on a new constitutive model of liquids. Three possible mathematical formalisms have been considered related to this physical formalism, i.e to the theory of electroviscoelasticity: the first is tension tensor model, the second is Van del Pol derivative model and the third model is Van der pol derivative model of non-integer (fractional) order. The fractional integro-differential operators –(fractional calculus) is a generalization of integration and derivation to non-integer order (fractional) operators. Fractional derivatives/integrals provide an excellent instrument for the description of memory and heretidary properties of various materials and processes and, also obtaining more degrees of freedom in the model. In this paper, central parts of presentation will be solution using Caputo definition of fractional operators to ...obtain a (non)homogeneuos solution of a (nonlinear) equation of Van der Pol of non-integer order where it willbwe discussed a cases of the (alpha,beta) order, variable order approach alpha=alpha(t) and generalized differential transforms method. Finally, it is proposed adequate algorithms using a predictor-corrector approach and approximations of fractional derivatives/integrals.
Кључне речи:
electroviscoelasticity / van der Pol type / liquid/liquid interfaces / fractional orderИзвор:
Book of abstracts MASSEE Int Congress on Mathematics MICOM2009, Sept. 16-20 2009, Ohrid, Macedonia, 2009, 63-63Издавач:
- Mathematical Society of South-Eastern Europe
- Union of Mathematicans of Macedonia
Колекције
Институција/група
Mašinski fakultetTY - CONF AU - Lazarević, Mihailo AU - Spasić, Aleksandar AU - Bučanović, Ljubiša PY - 2009 UR - https://machinery.mas.bg.ac.rs/handle/123456789/6601 AB - A new, recently developed, theory of electroviscoelasticity describes the behavior of electrified liquid-liquid interfaces in fine dispersed systems, and is based on a new constitutive model of liquids. Three possible mathematical formalisms have been considered related to this physical formalism, i.e to the theory of electroviscoelasticity: the first is tension tensor model, the second is Van del Pol derivative model and the third model is Van der pol derivative model of non-integer (fractional) order. The fractional integro-differential operators –(fractional calculus) is a generalization of integration and derivation to non-integer order (fractional) operators. Fractional derivatives/integrals provide an excellent instrument for the description of memory and heretidary properties of various materials and processes and, also obtaining more degrees of freedom in the model. In this paper, central parts of presentation will be solution using Caputo definition of fractional operators to obtain a (non)homogeneuos solution of a (nonlinear) equation of Van der Pol of non-integer order where it willbwe discussed a cases of the (alpha,beta) order, variable order approach alpha=alpha(t) and generalized differential transforms method. Finally, it is proposed adequate algorithms using a predictor-corrector approach and approximations of fractional derivatives/integrals. PB - Mathematical Society of South-Eastern Europe PB - Union of Mathematicans of Macedonia C3 - Book of abstracts MASSEE Int Congress on Mathematics MICOM2009, Sept. 16-20 2009, Ohrid, Macedonia T1 - Fractional order Van der Pol model of electroviscoelasticity of liquid/liquid interfaces: analytical and numerical solution EP - 63 SP - 63 UR - https://hdl.handle.net/21.15107/rcub_machinery_6601 ER -
@conference{ author = "Lazarević, Mihailo and Spasić, Aleksandar and Bučanović, Ljubiša", year = "2009", abstract = "A new, recently developed, theory of electroviscoelasticity describes the behavior of electrified liquid-liquid interfaces in fine dispersed systems, and is based on a new constitutive model of liquids. Three possible mathematical formalisms have been considered related to this physical formalism, i.e to the theory of electroviscoelasticity: the first is tension tensor model, the second is Van del Pol derivative model and the third model is Van der pol derivative model of non-integer (fractional) order. The fractional integro-differential operators –(fractional calculus) is a generalization of integration and derivation to non-integer order (fractional) operators. Fractional derivatives/integrals provide an excellent instrument for the description of memory and heretidary properties of various materials and processes and, also obtaining more degrees of freedom in the model. In this paper, central parts of presentation will be solution using Caputo definition of fractional operators to obtain a (non)homogeneuos solution of a (nonlinear) equation of Van der Pol of non-integer order where it willbwe discussed a cases of the (alpha,beta) order, variable order approach alpha=alpha(t) and generalized differential transforms method. Finally, it is proposed adequate algorithms using a predictor-corrector approach and approximations of fractional derivatives/integrals.", publisher = "Mathematical Society of South-Eastern Europe, Union of Mathematicans of Macedonia", journal = "Book of abstracts MASSEE Int Congress on Mathematics MICOM2009, Sept. 16-20 2009, Ohrid, Macedonia", title = "Fractional order Van der Pol model of electroviscoelasticity of liquid/liquid interfaces: analytical and numerical solution", pages = "63-63", url = "https://hdl.handle.net/21.15107/rcub_machinery_6601" }
Lazarević, M., Spasić, A.,& Bučanović, L.. (2009). Fractional order Van der Pol model of electroviscoelasticity of liquid/liquid interfaces: analytical and numerical solution. in Book of abstracts MASSEE Int Congress on Mathematics MICOM2009, Sept. 16-20 2009, Ohrid, Macedonia Mathematical Society of South-Eastern Europe., 63-63. https://hdl.handle.net/21.15107/rcub_machinery_6601
Lazarević M, Spasić A, Bučanović L. Fractional order Van der Pol model of electroviscoelasticity of liquid/liquid interfaces: analytical and numerical solution. in Book of abstracts MASSEE Int Congress on Mathematics MICOM2009, Sept. 16-20 2009, Ohrid, Macedonia. 2009;:63-63. https://hdl.handle.net/21.15107/rcub_machinery_6601 .
Lazarević, Mihailo, Spasić, Aleksandar, Bučanović, Ljubiša, "Fractional order Van der Pol model of electroviscoelasticity of liquid/liquid interfaces: analytical and numerical solution" in Book of abstracts MASSEE Int Congress on Mathematics MICOM2009, Sept. 16-20 2009, Ohrid, Macedonia (2009):63-63, https://hdl.handle.net/21.15107/rcub_machinery_6601 .