Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
In this paper the quasilinearization method is extended to finite systems of Riemann-Liouville fractional differential equations of order 0 < q < 1. Existence and comparison results of the linear Riemann-Liouville fractional differential systems are recalled and modified where necessary. Using upper and lower solutions, sequences are constructed that are monotonic such that the weighted sequences converge uniformly and quadratically to the unique solution of the system. A numerical example illustrating the main result is given.
Czasopismo
Rocznik
Tom
Strony
667–--683
Opis fizyczny
Bibliogr. 31 poz.
Twórcy
autor
- North Carolina A&T State University Department of Mathematics and Statistics 1601 E Market St, Greensboro, NC 27411, USA
autor
- Brenau University Department of Mathematics and Science 500 Washington St SE, Gainesville, GA 30501, USA
Bibliografia
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- [6] E.A. Boroujeni, H.R. Momeni, Observer based control of a class of nonlinear fractional-order systems using lmi, International Journal of Science and Engineering Investigations 1 (2012) 1, 48-52.
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- [8] A. Chikrii, S. Eidelman, Generalized Mittag-Leffler matrix functions in game problems for evolutionary equations of fractional order, Cybern. Syst. Analysis 36 (2000) 3, 315-338.
- [9] A. Chikrii, I. Matichin, Presentation of solutions of linear systems with fractional derivatives in the sense of Riemann-Liouvil le, Caputo, and Mil ler-Ross, J. Autom. Inf. Sci. 40 (2008) 6, 1-11.
- [10] A. Chowdhury, C.I. Christov, Memory effects for the heat conductivity of random suspensions of spheres, Proc. R. Soc. A 466 (2010), 3253-3273.
- [11] L. Debnath, Recent applications of fractional calculus to science and engineering, International Journal of Mathematics and Mathematical Sciences 54 (2003), 3413-3442.
- [12] Z. Denton, Generalized extension of the quasilinearization for Riemann-Liouvil le fractional differential equations, Dynamic Systems and Applications 23 (2014) 2 & 3, 333-350.
- [13] Z. Denton, P.W. Ng, A.S. Vatsala, Quasilinearization method via lower and upper solutions for Riemann-Liouvil le fractional differential equations, Nonlinear Dynamics and Systems Theory 11 (2011) 3, 239-251.
- [14] Z. Denton, J.D. Ramhez, Monotone method for finite systems of nonlinear
- Riemann-Liouvil le fractional integro-differential equations, Nonlinear Dynamics and Systems Theory 18 (2018) 2, 130-143.
- [15] Z. Denton, A.S. Vatsala, Monotone iterative technique for finite systems of nonlinear Riemann-Liouville fractional differential equations, Opuscula Math. 31 (2011) 3, 327-339.
- [16] Z. Denton, A.S. Vatsala, Generalized quasilinearization method for RL fractional differential equations, Nonlinear Studies 19 (2012) 4, 637-652.
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- [19] W.G. Glockle, T.F. Nonnenmacher, A fractional calculus approach to self similar protein dynamics, Biophy. J. 68 (1995), 46-53.
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Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-8758dc64-bbf6-4334-b749-9e850b4f0bc5