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International Journal of Differential Equations
Volume 2016, Article ID 9815796, 6 pages
http://dx.doi.org/10.1155/2016/9815796
Research Article

About a Problem for Loaded Parabolic-Hyperbolic Type Equation with Fractional Derivatives

1Department of Functional Analysis and Integral Equations, University of Las Palmas de Gran Canaria, Campus de Tafira Baja, Las Palmas, 35017 Gran Canaria, Spain
2Faculty of Mechanics-Mathematics, Department of Differential Equations and Mathematical Physics, National University of Uzbekistan, Universitetskaya 4, Almazar, 100125 Tashkent, Uzbekistan

Received 12 February 2016; Revised 7 June 2016; Accepted 29 June 2016

Academic Editor: Nikolai A. Kudryashov

Copyright © 2016 Kishin B. Sadarangani and Obidjon Kh. Abdullaev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. F. Mainardi, “Fractional calculus: some basic problem in continuum and statistical mechanics,” in Fractal and Fractional Calculus in Continuum Mechanics, A. Carpinteri and F. Mainardi, Eds., pp. 291–948, Sprienger, Vienna, Austria, 1997. View at Google Scholar
  2. A. I. Saichev and G. M. Zaslavsky, “Fractional kinetic equations: solutions and applications,” Chaos, vol. 7, no. 4, pp. 753–764, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  3. W. Wyss, “The fractional diffusion equation,” Journal of Mathematical Physics, vol. 27, no. 11, pp. 2782–2785, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  4. A. A. Kilbas and O. A. Repin, “An analog of the Tricomi problem for a mixed type equation with a partial fractional derivative,” Fractional Calculus & Applied Analysis, vol. 13, no. 1, pp. 69–84, 2010. View at Google Scholar
  5. V. A. Nakhusheva, “Boundary problems for mixed type heat equation,” Doklady AMAN, vol. 12, no. 2, pp. 39–44, 2010 (Russian). View at Google Scholar
  6. E. Y. Arlanova, “A problem with a shift for the mixed type equation with the generalized operators of fractional integration and differentiation in a boundary condition,” Vestnik Samarsk Gosudarstvennogo Universiteta, vol. 6, no. 65, pp. 396–406, 2008 (Russian). View at Google Scholar
  7. A. A. Kilbas and O. A. Repin, “An analog of the Bitsadze-Samarskii problem for a mixed type equation with a fractional derivative,” Differentsial'nye Uravneniya, vol. 39, no. 5, pp. 638–719, 2003, Translation in Journal of Difference Equations and Applications, vol. 39, no. 5, pp. 674–680, 2003. View at Google Scholar
  8. B. J. Kadirkulov, “Boundary problems for mixed parabolic-hyperbolic equations with two lines of changing type and fractional derivative,” Electronic Journal of Differential Equations, vol. 2014, no. 57, pp. 1–7, 2014. View at Google Scholar
  9. E. T. Karimov and J. S. Akhatov, “A boundary problem with integral gluing condition for a parabolic-hyperbolic equation involving the Caputo fractional derivative,” Electronic Journal of Differential Equations, vol. 2014, no. 14, pp. 1–6, 2014. View at Google Scholar · View at MathSciNet
  10. A. M. Nakhushev, The Loaded Equations and Their Applications, M. Nauka, 2012.
  11. V. A. Eleev, “About some boundary value problems for mixed type loaded equations of the second and third equations,” Differential Equations, vol. 30, no. 2, pp. 230–237, 1994. View at Google Scholar
  12. V. М. Kaziev, “On a Darboux problem for the one loaded integral-differential equations of the second order,” Differential Equations, vol. 14, no. 1, pp. 181–184, 1978. View at Google Scholar
  13. I. N. Lanin, “Boundary value problems for the loaded hyperbolic-parabolic type equations of the third equations,” Differential Equations, vol. 17, no. 1, pp. 97–106, 1981. View at Google Scholar
  14. O. Kh. Abdullaev, “Boundary value problem for a loaded equation elliptic-hyperbolic type in double connected domain,” Journal Collection of Scientific Works of KRASEC, vol. 1, no. 8, 2014. View at Google Scholar
  15. O. Kh. Abdullaev, “About a method of research of the non-local problem for the loaded mixed type equation in double-connected domain,” Bulletin of KRASEC: Physical & Mathematical Sciences, vol. 9, no. 2, pp. 11–16, 2014. View at Google Scholar
  16. O. Kh. Abdullaev, “Non-local boundary value problem for the mixed type equations on the third order in double-connected domains,” Journal of PDE, vol. 27, no. 4, pp. 283–292, 2014. View at Google Scholar
  17. O. Kh. Abdullaev, “Non-local problem for the loaded mixed type equation with the integrated operators,” in Proceedings of the International Conference. Differential Equations and Mathematical Modelin, pp. 21–23, Ulan-Ude, Russia, 2015.
  18. A. V. Pskhu, “Solution of boundary value problems fractional diffusion equation by the green function method,” Differential Equation, vol. 39, no. 10, pp. 1509–1513, 2003. View at Google Scholar
  19. M. M. Smirnov, Mixed Type Equations, Nauka, Moscow, Russia, 2000.
  20. A. V. Pskhu, Partial Differential Equation of Fractional Order, Nauka, Moscow, Russia, 2005 (Russian).
  21. B. J. Кadirkulov and B. Kh. Turmetov, “On a generalization of the heat equation,” UzMJ, no. 3, pp. 40–46, 2006, http://uzmj.mathinst.uz/files/uzmj-2006_3.pdf. View at Google Scholar