- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- 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 2010 (2010), Article ID 649486, 10 pages
Solvability of Nonlinear Langevin Equation Involving Two Fractional Orders with Dirichlet Boundary Conditions
1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782 Santiago de Compostela, Spain
Received 8 August 2009; Accepted 14 November 2009
Academic Editor: Nikolai Leonenko
Copyright © 2010 Bashir Ahmad and Juan J. Nieto. 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.
- A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science B. V., Amsterdam, The Netherlands, 2006.
- V. Lakshmikantham, S. Leela, and J. Vasundhara Devi, Theory of Fractional Dynamic Systems, Cambridge Academic, Cambridge, UK, 2009.
- I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, Calif., USA, 1999.
- B. Ahmad and J. J. Nieto, “Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions,” Boundary Value Problems, vol. 2009, Article ID 708576, 11 pages, 2009.
- B. Ahmad and J. J. Nieto, “Existence of solutions for nonlocal boundary value problems of higher-order nonlinear fractional differential equations,” Abstract and Applied Analysis, vol. 2009, Article ID 494720, 9 pages, 2009.
- B. Ahmad and J. J. Nieto, “Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions,” Computers & Mathematics with Applications, vol. 58, no. 9, pp. 1838–1843, 2009.
- B. Ahmad and J. J. Nieto, “Existence of solutions for anti-periodic boundary value problems involving fractional differential equations via Leray-Schauder degree theory,” to appear in Topological Methods in Nonlinear Analysis.
- B. Ahmad, “Existence of solutions for irregular boundary value problems involving nonlinear fractional differential equations,” Applied Mathematics Letters, 2009.
- B. Ahmad and J. J. Nieto, “Existence of solutions for impulsive anti-periodic boundary value problems of fractional order,” to appear in Taiwanese Journal of Mathematics.
- Y.-K. Chang and J. J. Nieto, “Some new existence results for fractional differential inclusions with boundary conditions,” Mathematical and Computer Modelling, vol. 49, no. 3-4, pp. 605–609, 2009.
- V. Daftardar-Gejji and S. Bhalekar, “Boundary value problems for multi-term fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 345, no. 2, pp. 754–765, 2008.
- R. Hilfer, Ed., Applications of Fractional Calculus in Physics, World Scientific, River Edge, NJ, USA, 2000.
- S. Z. Rida, H. M. El-Sherbiny, and A. A. M. Arafa, “On the solution of the fractional nonlinear Schrödinger equation,” Physics Letters A, vol. 372, no. 5, pp. 553–558, 2008.
- A. Arara, M. Benchohra, N. Hamidi, and J. J. Nieto, “Fractional order differential equations on an unbounded domain,” Nonlinear Analysis, vol. 72, pp. 580–586, 2010.
- D. Baleanu, A. K. Golmankhaneh, and A. K. Golmankhaneh, “Fractional Nambu mechanics,” International Journal of Theoretical Physics, vol. 48, no. 4, pp. 1044–1052, 2009.
- M. R. Ubriaco, “Entropies based on fractional calculus,” Physics Letters A, vol. 373, no. 30, pp. 2516–2519, 2009.
- W. T. Coffey, Yu. P. Kalmykov, and J. T. Waldron, The Langevin Equation: With Applications to Stochastic Problems in Physics, Chemistry and Electrical Engineering, vol. 14 of World Scientific Series in Contemporary Chemical Physics, World Scientific, River Edge, NJ, USA, 2nd edition, 2004.
- S. C. Lim, M. Li, and L. P. Teo, “Langevin equation with two fractional orders,” Physics Letters A, vol. 372, no. 42, pp. 6309–6320, 2008.
- S. C. Lim and L. P. Teo, “The fractional oscillator process with two indices,” Journal of Physics A, vol. 42, no. 6, Article ID 065208, 34 pages, 2009.
- D. R. Smart, Fixed Point Theorems, Cambridge University Press, Cambridge, UK, 1980.