RUS  ENG
Full version
JOURNALS // Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences

Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2014, Issue 1(34), Pages 134–144 (Mi vsgtu1272)

Development of Identification Methods for Fractional Differential Equations with Riemann–Liouville Fractional Derivative
A. S. Ovsienko

References

1. K. B. Oldham, J. Spanier, The fractional calculus. Theory and applications of differentiation and integration to arbitrary order, Mathematics in Science and Engineering, 111, Academic Press, New York, London, 1974, xiii+234 pp.  mathscinet  zmath
2. K. S. Miller, B. Ross, An introduction to the fractional calculus and fractional differential equations, Jon Wiley & Sons. Inc., New York, 1993, xiii+366 pp.  mathscinet  zmath
3. A. M. Nakhushev, Uravneniya matematicheskoy biologii [Equations of mathematical biology], Vysshaya Shkola, Moscow, 1995, 301 pp. (In Russian)  zmath
4. R. Gorenflo, F. Mainardi, “Fractional calculus, integral and differential equations of fractional order”, Fractals and Fractional Calculus in Continuum Mechanics, Courses and Lecture Notes, 378, Springer Verlag, Wien, New York, 1997, 223–276, arXiv: 0805.3823 [math-ph]  crossref  mathscinet
5. I. Podlubny, Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Mathematics in Science and Engineering, 198, Academic Press, San Diego, 1999, xxiv+340 pp.  mathscinet  zmath
6. V. V. Uchaikin, Metod drobnykh proizvodnykh [The method of fractional derivatives], Artichoke Publ., Ulyanovsk, 2008, 512 pp.
7. A. M. Nakhushev, Elementy drobnogo ischisleniya i ikh primenenie [Elements of Fractional Calculus and Their Application], Kabardino-Balkarsk. Nauchn. Tsentr Ross. Akad. Nauk, Nalchik, 2003, 299 pp. (In Russian)
8. A. M. Nakhushev, Drobnoe ischislenie i ego primenenie [Fractional calculus and its applications], Fizmatlit, Moscow, 2003, 271 pp. (In Russian)  zmath
9. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, Elsevier, Amsterdam, 204, xv+523 pp.  mathscinet  zmath
10. V. V. Vasilyev, L. O. Simak, Drobnoe ischislenie i approksimatsionnye metody v modelirovanii dinamicheskikh sistem [Fractional calculus and approximation methods for modeling of dynamic systems], NAN Ukraine, Kiev, 2008, 256 pp. (In Russian)
11. S. Das, Functional Fractional Calculus, Springer-Verlag, Berlin, Heidelberg, 2011, ix+612 pp.  crossref  mathscinet  zmath
12. A. S. Ovsienko, “Development of parameter identification method for fractional differential operator”, Proceedings of the Eighth All-Russian Scientific Conference with international participation. Part 2, Matem. Mod. Kraev. Zadachi, Samara State Technical Univ., Samara, 2011, 195–201 (In Russian)
13. A. S. Ovsienko, “Parametric identification of Cauchy problem for one fractional differential equation”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2012, no. 1(26), 157–165 (In Russian)  mathnet  crossref  rsci
14. J. H. Barrett, “Differential equations of non-integer order”, Canad. J. Math., 6:4 (1954), 529–541  crossref  mathscinet  zmath
15. E. N. Ogorodnikov, V. P. Radchenko, N. S. Yashagin, “Rheological model of viscoelastic body with memory and differential equations of fractional oscillator”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2011, no. 1(22), 255–268 (In Russian)  mathnet  crossref  rsci
16. E. N. Ogorodnikov, “Some Aspects of Initial Value Problems Theory for Differential Equations with Riemann–Liouville Derivatives”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2010, no. 5(21), 10–23 (In Russian)  mathnet  crossref  rsci
17. M. M. Dzrbasjan, Integralnye preobrazovaniya i predstavleniya funktsiy v kompleksnoy oblasti [Integral Transforms and Representations of Functions in Complex Domain], Nauka, Moscow, 1966, 672 pp. (In Russian)  mathscinet
18. V. E. Zoteev, Parametricheskaya identifikatsiya dissipativnykh mekhanicheskikh sistem na osnove raznostnykh uravneniy [Parametric identification of dissipative mechanical systems on the basis of difference equations], ed. V. P. Radchenko, Mashinostroenie-1, Moscow, 2009, 344 pp. (In Russian)  elib
19. A. S. Ovsienko, “Parameter identification of anomalous diffusion process on the basis of difference equation”, Vychislitelnye tekhnologii, 18:1 (2013), 65–73 (In Russian)  elib
20. N. N. Kalitkin, Chislennye metody [Numerical Methods], Nauka, Moscow, 1978, 512 pp. (In Russian)  mathscinet


© Steklov Math. Inst. of RAS, 2025