Abstract:
Some special functions, concerning Mittag–Leffler type function, are introduced. The solution to Cauchy problem for some linear non-homogeneous fractional oscillating equation in terms of these functions are given.
Keywords:
Mittag-Leffler type function, Rieman-Liouville's franctional integrals and derivates, Caushy problem for a fractional occilating equation.
Original article submitted 05/X/2008 revision submitted – 12/II/2009
Citation:
E. N. Ogorodnikov, N. S. Yashagin, “Some Special Functions in the Solution To Cauchy Problem for a Fractional Oscillating Equation”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(18) (2009), 276–279
\Bibitem{OgoYas09}
\by E.~N.~Ogorodnikov, N.~S.~Yashagin
\paper Some Special Functions in the Solution To Cauchy Problem for a Fractional Oscillating Equation
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2009
\vol 1(18)
\pages 276--279
\mathnet{http://mi.mathnet.ru/vsgtu685}
\crossref{https://doi.org/10.14498/vsgtu685}
Linking options:
https://www.mathnet.ru/eng/vsgtu685
https://www.mathnet.ru/eng/vsgtu/v118/p276
This publication is cited in the following 21 articles:
E. N. Ogorodnikov, V. P. Radchenko, L. G. Ungarova, “Mathematical models of nonlinear viscoelasticity with operators of fractional integro-differentiation”, PNRPU Mechanics Bulletin, 2018, no. 2, 147–161 (In Russian)
E. N. Ogorodnikov, V. P. Radchenko, L. G. Ungarova, “Matematicheskoe modelirovanie nasledstvenno uprugogo deformiruemogo tela
na osnove strukturnykh modelei i apparata drobnogo
integro-differentsirovaniya Rimana–Liuvillya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 20:1 (2016), 167–194
L. G. Ungarova, “Primenenie lineinykh drobnykh analogov reologicheskikh modelei v zadache approksimatsii eksperimentalnykh dannykh
po rastyazheniyu polivinilkhloridnogo plastikata”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 20:4 (2016), 691–706
E. N. Ogorodnikov, “Ob odnom klasse drobnykh differentsialnykh uravnenii matematicheskikh modelei dinamicheskikh sistem s pamyatyu”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(30) (2013), 245–252
E. N. Ogorodnikov, “Postanovka i reshenie zadachi tipa Koshi dlya odnogo klassa modelnykh dinamicheskikh sistem s pamyatyu”, Trudy devyatoi Vserossiiskoi nauchnoi konferentsii s mezhdunarodnym uchastiem. Chast 1, Matematicheskoe modelirovanie i kraevye zadachi, SamGTU, Samara, 2013, 147–152
A. S. Ovsienko, “Parametricheskaya identifikatsiya zadachi tipa Koshi dlya odnogo drobnogo differentsialnogo uravneniya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(26) (2012), 157–165
E. N. Ogorodnikov, “O dvukh spetsialnykh funktsiyakh, obobschayuschikh funktsiyu tipa Mittag–Lefflera, ikh svoistvakh i primenenii”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(26) (2012), 52–65
E. N. Ogorodnikov, “Dve spetsialnye funktsii tipa obobschennoi funktsii Mittag–Lefflera v resheniyakh integralnykh i differentsialnykh uravnenii s operatorami Rimana–Liuvillya i Kobera”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 3(28) (2012), 30–40
L. G. Abusaitova, E. N. Ogorodnikov, “O nekotorykh spetsialnykh funktsiyakh, svyazannykh s funktsiei Mittag–Lefflera, ikh svoistvakh i primenenii”, Nelokalnye kraevye zadachi i problemy sovremennogo analiza i informatiki Materialy Kh Shkoly molodykh uchenykh, Materialy Kh Shkoly molodykh uchenykh. 2012 (Elbrus, 28 maya–01 iyunya 2012 g.), Kabardino-Balkarskii nauchnyi tsentr RAN, Nalchik, 2012, 13–15
E. N. Ogorodnikov, V. P. Radchenko, N. S. Yashagin, “Reologicheskie modeli vyazkouprugogo tela s pamyatyu i differentsialnye uravneniya drobnykh ostsillyatorov”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(22) (2011), 255–268
E. N. Ogorodnikov, “O nachalnykh zadachakh dlya differentsialnykh uravnenii s drobnymi proizvodnymi Rimana—Liuvillya”, Materialy Vtorogo Mezhdunarodnogo Rossiisko–Kazakhskogo simpoziuma «Uravneniya smeshannogo tipa, rodstvennye problemy analiza i informatiki», sbornik trudov konferentsii (Nalchik, 23–27 maya 2011 g.), Kabardino-Balkarskii nauchnyi tsentr RAN, Nalchik, 2011, 131–134
E. N. Ogorodnikov, N. S. Yashagin, “Postanovka i reshenie zadach tipa Koshi dlya differentsialnykh uravnenii vtorogo poryadka s drobnymi proizvodnymi Rimana–Liuvillya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(20) (2010), 24–36
E. N. Ogorodnikov,N. S. Yashagin, “O postanovke i reshenii nachalnykh zadach dlya differentsialnykh uravnenii vtorogo poryadka s mladshimi proizvodnymi”, Trinadtsyata mizhnarodna naukova konferentsiya imeni akademika M. Kravchuka. T. 1, Materiali konf. (13–15 travnya, 2010), NTUU, Kiїv, 2010, 297–298
V. P. Radchenko, E. N. Ogorodnikov,N. S. Yashagin, “Matematicheskie modeli vyazko-uprugogo tela i vynuzhdennye kolebaniya drobnykh ostsillyatorov”, Trinadtsyata mizhnarodna naukova konferentsiya imeni akademika M. Kravchuka. T. 1, Materiali konf. (13–15 travnya, 2010), NTUU, Kiїv, 2010, 344–345
V. A. Vlasenko, E. N. Ogorodnikov, N. C. Yashagin, “Analiz vynuzhdennykh kolebanii drobnykh ostsillyatorov pod deistviem impulsnykh nagruzok”, Estvestvennye nauki. Chasti 1–3, Matematika, matematicheskoe modelirovanie, mekhanika, Aktualnye problemy sovremennoi nauki, SamGTU, Samara, 2010, 23–25
N. S. Yashagin, E. N. Ogorodnikov, “Ob odnom obobschenii funktsii tipa Mittag—Lefflera, integralnom operatore s ukazannoi funktsiei v yadre, ikh svoistvakh i prilozheniyakh”, Estvestvennye nauki. Chasti 1–3, Matematika, matematicheskoe modelirovanie, mekhanika, Aktualnye problemy sovremennoi nauki, SamGTU, Samara, 2010, 261–267
E. N. Ogorodnikov, “Nekotorye aspekty teorii nachalnykh zadach dlya differentsialnykh uravnenii s proizvodnymi Rimana–Liuvillya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 5(21) (2010), 10–23
E. N. Ogorodnikov, N. S. Yashagin, “Suschestvovanie, edinstvennost i struktura resheniya zadachi Koshi dlya odnogo klassa obyknovennykh lineinykh differentsialnykh uravnenii s drobnymi proizvodnymi Rimana–Liuvillya”, Trudy sedmoi Vserossiiskoi nauchnoi konferentsii s mezhdunarodnym uchastiem (3–6 iyunya 2010 g.). Chast 3, Differentsialnye uravneniya i kraevye zadachi, Matem. modelirovanie i kraev. zadachi, Samarskii gosudarstvennyi tekhnicheskii universitet, Samara, 2010, 225–232
E. N. Ogorodnikov, “Matematicheskie modeli drobnykh ostsillyatorov, postanovka i struktura resheniya zadachi Koshi”, Trudy shestoi Vserossiiskoi nauchnoi konferentsii s mezhdunarodnym uchastiem (1–4 iyunya 2009 g.). Chast 1, Matematicheskie modeli mekhaniki, prochnosti i nadezhnosti elementov konstruktsii, Matem. modelirovanie i kraev. zadachi, SamGTU, Samara, 2009, 177–181
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