- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
International Journal of Differential Equations
Volume 2011 (2011), Article ID 268465, 10 pages
Boundary Value Problems with Integral Gluing Conditions for Fractional-Order Mixed-Type Equation
1Kazakh National Pedagogical University named after Abai, 050010 Almaty, Kazakhstan
2University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
Received 18 May 2011; Accepted 11 October 2011
Academic Editor: Shaher M. Momani
Copyright © 2011 A. S. Berdyshev et al. 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.
- I. M. Gel'fand, “Some questions of analysis and differential equations,” Uspekhi Matematicheskikh Nauk, vol. 3, no. 87, pp. 3–19, 1959 (Russian).
- V. A. Nakhusheva, Differential Equations of Mathematical Models of Non-Local Processes, Nauka, Moscow, Russia, 2006 (Russian).
- T. D. Djuraev, A. Sopuev, M. Mamajonov, et al., Boundary Value Problems for Parabolic-Hyperbolic Type Equations, Fan, Tashkent, Uzbekistan, 1986 (Russian).
- A. M. Nakhushev, Problems with Displacements for Partial Differential Equations, Nauka, Moscow, Russia, 2006 (Russian).
- 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.
- V. A. Nakhusheva, “Boundary problems for mixed type heat equation,” Doklady AMAN, vol. 12, no. 2, pp. 39–44, 2010 (Russian).
- 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).
- A. A. Kilbas and O. A. Repin, “An analogue of the Bitsadze-Samarskiĭ problem for an equation of mixed type 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.
- A. V. Efimov, “On boundary value problems with Saigo operators for the mixed type equation with a fractional derivative,” Vestnik Samarsk, Georgian Technical University, vol. 26, pp. 16–20, 2004 (Russian).
- S. K. Gekkieva, “A boundary value problem for the generalized transfer equation with a fractional derivative in a semi-infinite domain,” Izvestiya Kabardino-Balkarskaya Nauchnoogo Tsentra RAN, vol. 8, no. 1, pp. 6–8, 2002 (Russian).
- S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach Science, Yverdon, Switzerland, 1993, Edited and with a foreword by S. M. Nikol'skiĭ. Translated from the 1987 Russian original.
- I. Podlubny, Fractional Differential Equations, vol. 198, Academic Press, San Diego, CA, USA, 1999.
- A. M. Nakhushev, Fractional Calculus and its Applications, Fizmatlit, Moscow, Russia, 2003.
- A. V. Pskhu, Partial Differential Equations of Fractional Order, Nauka, Moscow, Russia, 2005.
- A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204, Elsevier, Amsterdam, The Netherlands, 2006.
- R. Gorenflo and F. Mainardi, “Some recent advances in theory and simulation of fractional diffusion processes,” Journal of Computational and Applied Mathematics, vol. 229, no. 2, pp. 400–415, 2009.
- Y. Luchko, “Initial-boundary problems for the generalized multi-term time-fractional diffusion equation,” Journal of Mathematical Analysis and Applications, vol. 374, no. 2, pp. 538–548, 2011.
- W. Chen, H. Sun, X. Zhang, and D. Korošak, “Anomalous diffusion modeling by fractal and fractional derivatives,” Computers & Mathematics with Applications, vol. 59, no. 5, pp. 1754–1758, 2010.
- N. Yu. Kapustin and E. I. Moiseev, “On spectral problems with a spectral parameter in the boundary condition,” Differentsial'nye Uravneniya, vol. 33, no. 1, pp. 115–143, 1997, Translation in Differential Equations, vol. 33, no. 1, pp. 116–120, 1997.
- B. E. Eshmatov and E. T. Karimov, “Boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations,” Central European Journal of Mathematics, vol. 5, no. 4, pp. 741–750, 2007.
- A. G. Shashkov, System-Structural Analysis of the Heat Exchange Processes and Its Application, Moscow, Russia, 1983.
- E. T. Karimov, “Some non-local problems for the parabolic-hyperbolic type equation with complex spectral parameter,” Mathematische Nachrichten, vol. 281, no. 7, pp. 959–970, 2008.
- M. S. Salakhitdinov and A. K. Urinov, Boundary Value Problems for Equations of Mixed Type with a Spectral Parameter, Fan, Tashkent, Uzbekistan, 1997.
- A. V. Pskhu, “Solution of boundary value problems for a diffusion equation of fractional order by the Green's function method,” Differentsial'nye Uravneniya, vol. 39, no. 10, pp. 1430–1440, 2003.
- E. M. Wright, “The generalized Bessel function of order greater than one,” The Quarterly Journal of Mathematics, vol. 11, pp. 36–48, 1940.
- M. L. Krasnov, Integral Equations: Introduction to the Theory, Nauka, Moscow, Russia, 1975, Selected topics in higher mathematics for engineers and technological university students.
- K. U. Khubiev, “Gellerstedt problem loaded mixed type equation with data on non-parallel characteristics,” Manual Templating Model, vol. 3, pp. 187–188, 2007 (Russian).
- E. I. Moiseev and N. O. Taranov, “Solution of a Gellerstedt problem for the Lavrent'ev-Bitsadze equation,” Differentsial'nye Uravneniya, vol. 45, no. 4, pp. 558–563, 2009.