Yan, Bo; He, Shaobo Dynamics and complexity analysis of the conformable fractional-order two-machine interconnected power system. (English) Zbl 1471.34104 Math. Methods Appl. Sci. 44, No. 3, 2439-2454 (2021). MSC: 34C60 34A08 34A45 34D45 34D05 34C23 34D08 34C28 PDFBibTeX XMLCite \textit{B. Yan} and \textit{S. He}, Math. Methods Appl. Sci. 44, No. 3, 2439--2454 (2021; Zbl 1471.34104) Full Text: DOI
Lichae, Bijan Hasani; Biazar, Jafar; Ayati, Zainab Asymptotic decomposition method for fractional order Riccati differential equation. (English) Zbl 1474.65262 Comput. Methods Differ. Equ. 9, No. 1, 63-78 (2021). MSC: 65L99 34A08 PDFBibTeX XMLCite \textit{B. H. Lichae} et al., Comput. Methods Differ. Equ. 9, No. 1, 63--78 (2021; Zbl 1474.65262) Full Text: DOI
Baleanu, Dumitru; Wu, Guo-Cheng; Zeng, Sheng-Da Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations. (English) Zbl 1374.34306 Chaos Solitons Fractals 102, 99-105 (2017). MSC: 34K37 34K23 34D05 34K60 37M05 PDFBibTeX XMLCite \textit{D. Baleanu} et al., Chaos Solitons Fractals 102, 99--105 (2017; Zbl 1374.34306) Full Text: DOI
Romanova, E. Yu. Spectral analysis of Dirac operator in Lebesgue spaces. (Russian. English summary) Zbl 1356.34086 Vestn. Voronezh. Gos. Univ., Ser. Fiz. Mat. 2015, No. 2, 142-149 (2015). MSC: 34L40 34L20 34L10 47B40 PDFBibTeX XMLCite \textit{E. Yu. Romanova}, Vestn. Voronezh. Gos. Univ., Ser. Fiz. Mat. 2015, No. 2, 142--149 (2015; Zbl 1356.34086)
Biazar, Jafar; Didgar, Mohsen Numerical solution of Riccati equations by the Adomian and asymptotic decomposition methods over extended domains. (English) Zbl 1339.34026 Int. J. Differ. Equ. 2015, Article ID 580741, 7 p. (2015). MSC: 34A45 34A34 65L05 PDFBibTeX XMLCite \textit{J. Biazar} and \textit{M. Didgar}, Int. J. Differ. Equ. 2015, Article ID 580741, 7 p. (2015; Zbl 1339.34026) Full Text: DOI
Romanova, E. Yu. Spectral analysis of a differential operator with involution. (Russian, English) Zbl 1349.34374 Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform. 14, No. 4, 64-78 (2014); translation in J. Math. Sci., New York 213, No. 6, 897-909 (2016). MSC: 34L05 34L20 34L10 47B40 PDFBibTeX XMLCite \textit{E. Yu. Romanova}, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform. 14, No. 4, 64--78 (2014; Zbl 1349.34374); translation in J. Math. Sci., New York 213, No. 6, 897--909 (2016) Full Text: DOI
Bougoffa, Lazhar On the solutions of an oxygen absorption model. (English) Zbl 1309.65087 Int. J. Biomath. 7, No. 6, Article ID 1450061, 6 p. (2014). MSC: 65L10 34B05 65L70 65Y20 PDFBibTeX XMLCite \textit{L. Bougoffa}, Int. J. Biomath. 7, No. 6, Article ID 1450061, 6 p. (2014; Zbl 1309.65087) Full Text: DOI
Ali, Javed; Islam, S.; Khan, Hamid; Shah, Syed Inayat Ali The optimal homotopy asymptotic method for the solution of higher-order boundary value problems in finite domains. (English) Zbl 1252.65126 Abstr. Appl. Anal. 2012, Article ID 401217, 14 p. (2012). MSC: 65L10 34B15 PDFBibTeX XMLCite \textit{J. Ali} et al., Abstr. Appl. Anal. 2012, Article ID 401217, 14 p. (2012; Zbl 1252.65126) Full Text: DOI
Shishkin, G. I.; Shishkina, L. P. Improved difference scheme of the solution decomposition method for a singularly perturbed reaction-diffusion equation. (English. Russian original) Zbl 1227.65067 Proc. Steklov Inst. Math. 272, Suppl. 1, 197-214 (2011); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 16, No. 1, 255-271 (2010). MSC: 65L12 65L11 34B10 34E15 65L20 PDFBibTeX XMLCite \textit{G. I. Shishkin} and \textit{L. P. Shishkina}, Proc. Steklov Inst. Math. 272, 197--214 (2011; Zbl 1227.65067); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 16, No. 1, 255--271 (2010) Full Text: DOI
Rach, Randolph; Duan, Jun-Sheng Near-field and far-field approximations by the Adomian and asymptotic decomposition methods. (English) Zbl 1209.65071 Appl. Math. Comput. 217, No. 12, 5910-5922 (2011). MSC: 65L05 34A34 34A25 PDFBibTeX XMLCite \textit{R. Rach} and \textit{J.-S. Duan}, Appl. Math. Comput. 217, No. 12, 5910--5922 (2011; Zbl 1209.65071) Full Text: DOI
Drăgănescu, G. E.; Bereteu, L.; Ercuţa, A.; Luca, G. Anharmonic vibrations of a nano-sized oscillator with fractional damping. (English) Zbl 1221.74059 Commun. Nonlinear Sci. Numer. Simul. 15, No. 4, 922-926 (2010). MSC: 74M25 34A08 74H10 74H25 26A33 PDFBibTeX XMLCite \textit{G. E. Drăgănescu} et al., Commun. Nonlinear Sci. Numer. Simul. 15, No. 4, 922--926 (2010; Zbl 1221.74059) Full Text: DOI
Feng, Zhaosheng; Gupta, Indranil Sen Korteweg-de Vries-Burgers equation with a higher-order nonlinearity. (English) Zbl 1213.34065 Differ. Equ. Dyn. Syst. 16, No. 1-2, 3-27 (2008). MSC: 34C37 34E05 35Q53 35C07 34B40 PDFBibTeX XMLCite \textit{Z. Feng} and \textit{I. S. Gupta}, Differ. Equ. Dyn. Syst. 16, No. 1--2, 3--27 (2008; Zbl 1213.34065) Full Text: DOI
Chandra Sekhara Rao, S.; Kumar, Mukesh Optimal B-spline collocation method for self-adjoint singularly perturbed boundary value problems. (English) Zbl 1119.65064 Appl. Math. Comput. 188, No. 1, 749-761 (2007). Reviewer: Srinivasan Natesan (Assam) MSC: 65L10 34B05 34E15 65L60 65L70 PDFBibTeX XMLCite \textit{S. Chandra Sekhara Rao} and \textit{M. Kumar}, Appl. Math. Comput. 188, No. 1, 749--761 (2007; Zbl 1119.65064) Full Text: DOI
Khuri, S. A. An alternative solution algorithm for the nonlinear generalized Emden-Fowler equation. (English) Zbl 1072.34503 Int. J. Nonlinear Sci. Numer. Simul. 2, No. 3, 299-302 (2001). MSC: 34A45 34E05 PDFBibTeX XMLCite \textit{S. A. Khuri}, Int. J. Nonlinear Sci. Numer. Simul. 2, No. 3, 299--302 (2001; Zbl 1072.34503) Full Text: DOI
Samojlenko, A. M. Asymptotic method for the investigation of \(m\)-frequency oscillation systems. (English. Russian original) Zbl 0942.34036 Ukr. Math. J. 50, No. 10, 1559-1585 (1998); translation from Ukr. Mat. Zh. 50, No. 10, 1366-1387 (1998). Reviewer: I.O.Parasyuk (Kyïv) MSC: 34C15 34E05 34C20 70K30 PDFBibTeX XMLCite \textit{A. M. Samojlenko}, Ukr. Mat. Zh. 50, No. 10, 1366--1387 (1998; Zbl 0942.34036); translation from Ukr. Mat. Zh. 50, No. 10, 1366--1387 (1998) Full Text: DOI
Lopatin, A. K. Normalization and averaging on compact Lie groups in nonlinear mechanics. (English) Zbl 0889.34039 Ukr. Mat. Zh. 49, No. 1, 47-67 (1997). Reviewer: I.O.Parasyuk (Kyïv) MSC: 34C29 34A45 34E05 22E05 34C15 PDFBibTeX XMLCite \textit{A. K. Lopatin}, Ukr. Mat. Zh. 49, No. 1, 47--67 (1997; Zbl 0889.34039) Full Text: DOI
Lopatin, A. K. Symmetry in perturbation problems. (English) Zbl 0947.37054 Shkil, Mykola (ed.) et al., Symmetry in nonlinear mathematical physics. Proceedings of the second international conference, Kyiv, Ukraine, July 7-13, 1997. Memorial Prof. W. Fushchych conference. Vol. 1. Kyiv: Institute of Mathematics of the National Academy of Sciences of Ukraine. 79-88 (1997). Reviewer: R.O.Popovych (Kyïv) MSC: 37K55 70H09 37K05 70H33 34C15 34C25 PDFBibTeX XMLCite \textit{A. K. Lopatin}, in: Symmetry in nonlinear mathematical physics. Proceedings of the second international conference, Kyiv, Ukraine, July 7--13, 1997. Memorial Prof. W. Fushchych conference. Vol. 1. Kyiv: Institute of Mathematics of the National Academy of Sciences of Ukraine. 79--88 (1997; Zbl 0947.37054)
Lopatin, A. K. Normalization and averaging on compact Lie groups in nonlinear mechanics. (English. Russian original) Zbl 0932.34041 Ukr. Math. J. 49, No. 1, 51-74 (1997); translation from Ukr. Mat. Zh. 49, No. 1, 47-67 (1997). MSC: 34C29 34A45 34E05 22E05 34C15 PDFBibTeX XMLCite \textit{A. K. Lopatin}, Ukr. Mat. Zh. 49, No. 1, 47--67 (1997; Zbl 0932.34041); translation from Ukr. Mat. Zh. 49, No. 1, 47--67 (1997) Full Text: DOI
Mitropolsky, Yu. A. Asymptotic decomposition method as development of Bogoliubov averaging method. (English) Zbl 0907.34031 Nonlinear Anal., Theory Methods Appl. 30, No. 8, 5203-5210 (1997). Reviewer: A.Martynyuk (Kyïv) MSC: 34C29 PDFBibTeX XMLCite \textit{Yu. A. Mitropolsky}, Nonlinear Anal., Theory Methods Appl. 30, No. 8, 5203--5210 (1997; Zbl 0907.34031) Full Text: DOI
Haldar, K.; Datta, B. K. Integrations by asymptotic decomposition. (English) Zbl 0855.34009 Appl. Math. Lett. 9, No. 2, 81-83 (1996). MSC: 34A25 34A45 PDFBibTeX XMLCite \textit{K. Haldar} and \textit{B. K. Datta}, Appl. Math. Lett. 9, No. 2, 81--83 (1996; Zbl 0855.34009) Full Text: DOI
Mitropolskyj, Yu. A.; Lopatin, A. K. Bogolyubov averaging and procedures of normalization in nonlinear mechanics. IV. (English) Zbl 0938.34030 Ukr. Math. J. 47, No. 8, 1005-1221 (1995) and Ukr. Mat. Zh. 47, No. 8, 1044-1068 (1995). Reviewer: I.O.Parasyuk (Kyïv) MSC: 34C20 34C29 34E05 34A30 37N15 74H10 PDFBibTeX XMLCite \textit{Yu. A. Mitropolskyj} and \textit{A. K. Lopatin}, Ukr. Mat. Zh. 47, No. 8, 1044--1068 (1995; Zbl 0938.34030)
Mitropol’skij, Yu. A.; Lopatin, A. K. Bogolyubov averaging and procedures of normalization in nonlinear mechanics. III. (English. Ukrainian original) Zbl 0946.34043 Ukr. Math. J. 46, No. 12, 1803-1826 (1994); translation from Ukr. Mat. Zh. 46, No. 12, 1627-1646 (1994). MSC: 34C29 34E10 PDFBibTeX XMLCite \textit{Yu. A. Mitropol'skij} and \textit{A. K. Lopatin}, Ukr. Mat. Zh. 46, No. 12, 1627--1646 (1994; Zbl 0946.34043); translation from Ukr. Mat. Zh. 46, No. 12, 1627--1646 (1994) Full Text: DOI
Mitropol’skij, Yu. A.; Lopatin, A. K. Bogolyubov averaging and normalization procedures in nonlinear mechanics. I. (English) Zbl 0851.70019 Ukr. Math. J. 46, No. 9, 1287-1306 (1994) and Ukr. Mat. Zh. 46, No. 9, 1171-1188 (1994). MSC: 70K99 34C29 PDFBibTeX XMLCite \textit{Yu. A. Mitropol'skij} and \textit{A. K. Lopatin}, Ukr. Mat. Zh. 46, No. 9, 1171--1188 (1994; Zbl 0851.70019)
Mitropol’skij, Yu. A.; Lopatin, A. K. Bogolyubov averaging and normalization procedures in nonlinear mechanics. I. (English) Zbl 0844.70017 Ukr. Mat. Zh. 46, No. 9, 1171-1188 (1994). MSC: 70K99 34C29 PDFBibTeX XMLCite \textit{Yu. A. Mitropol'skij} and \textit{A. K. Lopatin}, Ukr. Mat. Zh. 46, No. 9, 1171--1188 (1994; Zbl 0844.70017)
Danielyan, A. A.; Levitan, B. M.; Khasanov, A. B. Asymptotic behavior of Weyl-Titchmarsh \(m\)-function in the case of the Dirac system. (English. Russian original) Zbl 0743.34087 Math. Notes 50, No. 2, 816-823 (1991); translation from Mat. Zametki 50, No. 2, 67-76 (1991). Reviewer: V.N.Gusyatnikova (Pereslavl-Zalessky) MSC: 34L20 34B20 PDFBibTeX XMLCite \textit{A. A. Danielyan} et al., Math. Notes 50, No. 2, 816--823 (1991; Zbl 0743.34087); translation from Mat. Zametki 50, No. 2, 67--76 (1991) Full Text: DOI
Wu, Jianhong; Ruan, Shigui Asymptotic stability analysis for large scale neutral integrodifferential systems. (English) Zbl 0715.34128 Ann. Differ. Equations 6, No. 2, 217-224 (1990). MSC: 34K20 34K40 34D05 34D20 93D20 PDFBibTeX XMLCite \textit{J. Wu} and \textit{S. Ruan}, Ann. Differ. Equations 6, No. 2, 217--224 (1990; Zbl 0715.34128)
Mitropol’skij, Yu. A.; Lopatin, A. K. Asymptotic decomposition of completely integrable Pfaffian systems with small parameter. (English. Russian original) Zbl 0701.34053 Ukr. Math. J. 40, No. 3, 299-305 (1988); translation from Ukr. Mat. Zh. 40, No. 3, 349-356 (1988). Reviewer: I.Vrkoć MSC: 34C20 PDFBibTeX XMLCite \textit{Yu. A. Mitropol'skij} and \textit{A. K. Lopatin}, Ukr. Math. J. 40, No. 3, 299--305 (1988; Zbl 0701.34053); translation from Ukr. Mat. Zh. 40, No. 3, 349--356 (1988) Full Text: DOI
Mitropol’skij, Yu. A.; Lopatin, A. K. Asymptotic decomposition of differential systems with a small parameter. (English. Russian original) Zbl 0657.34043 Ukr. Math. J. 39, No. 2, 162-170 (1987); translation from Ukr. Mat. Zh. 39, No. 2, 194-204 (1987). Reviewer: J.H.Tian MSC: 34C29 PDFBibTeX XMLCite \textit{Yu. A. Mitropol'skij} and \textit{A. K. Lopatin}, Ukr. Math. J. 39, No. 2, 162--170 (1987; Zbl 0657.34043); translation from Ukr. Mat. Zh. 39, No. 2, 194--204 (1987) Full Text: DOI
Adomian, G. An investigation of the asymptotic decomposition method for nonlinear equations in physics. (English) Zbl 0637.65086 Appl. Math. Comput. 24, 1-17 (1987). Reviewer: Ju.V.Kostarčuk MSC: 65L99 65Z05 34E99 35B40 PDFBibTeX XMLCite \textit{G. Adomian}, Appl. Math. Comput. 24, 1--17 (1987; Zbl 0637.65086) Full Text: DOI
Dmitriev, M. G. Iterative solution of optimal control problems with fast and slow motions. (English. Russian original) Zbl 0548.49016 Sov. Math., Dokl. 28, 361-363 (1983); translation from Dokl. Akad. Nauk SSSR 272, 281-284 (1983). Reviewer: J.O’Reilly MSC: 90C55 34E05 65K10 49M27 93C15 93C99 PDFBibTeX XMLCite \textit{M. G. Dmitriev}, Sov. Math., Dokl. 28, 361--363 (1983; Zbl 0548.49016); translation from Dokl. Akad. Nauk SSSR 272, 281--284 (1983)
Fergola, P.; Tenneriello, C. Partial stability of composite systems with unstable subsystems. (English) Zbl 0512.93009 Large Scale Syst. 4, 101-105 (1983). MSC: 93A15 93D05 93D20 34D05 34D20 49M27 PDFBibTeX XMLCite \textit{P. Fergola} and \textit{C. Tenneriello}, Large Scale Syst. 4, 101--105 (1983; Zbl 0512.93009)
Peshatov, G. D. Generalization of the two-variable decomposition method. (English. Russian original) Zbl 0502.34043 Sov. Math. 25, No. 7, 99-103 (1981); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1981, No. 7(230), 85-88 (1981). MSC: 34E05 PDFBibTeX XMLCite \textit{G. D. Peshatov}, Sov. Math. 25, No. 7, 99--103 (1981; Zbl 0502.34043); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1981, No. 7(230), 85--88 (1981)
Grujic, Ljubomir T. Singular perturbations and large-scale systems. (English) Zbl 0411.93027 Int. J. Control 29, 159-169 (1979). MSC: 93D20 93D05 93A13 93A15 93C99 34E15 PDFBibTeX XMLCite \textit{L. T. Grujic}, Int. J. Control 29, 159--169 (1979; Zbl 0411.93027) Full Text: DOI