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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.
Citations to this Article [14 citations]
The following is the list of published articles that have cited the current article.
- Mokhtar Kirane, and Salman A. Malik, “The profile of blowing-up solutions to a nonlinear system of fractional differential equations,” Nonlinear Analysis-Theory Methods & Applications, vol. 73, no. 12, pp. 3723–3736, 2010.
- Anping Chen, and Yi Chen, “Existence of Solutions to Nonlinear Langevin Equation Involving Two Fractional Orders with Boundary Value Conditions,” Boundary Value Problems, 2011.
- Bashir Ahmad, Juan J. Nieto, Ahmed Alsaedi, and Moustafa El-Shahed, “A study of nonlinear Langevin equation involving two fractional orders in different intervals,” Nonlinear Analysis-Real World Applications, vol. 13, no. 2, pp. 599–606, 2012.
- Ali H. Bhrawy, and Mohammed A. Alghamdi, “A shifted Jacobi-Gauss-Lobatto collocation method for solving nonlinear fractional Langevin equation involving two fractional orders in different intervals,” Boundary Value Problems, 2012.
- Weerawat Sudsutad, and Jessada Tariboon, “Existence results of fractional integro-differential equations with m-point multi-term fractional order integral boundary conditions,” Boundary Value Problems, 2012.
- Bashir Ahmad, Juan J. Nieto, and Ahmed Alsaedi, “A nonlocal three-point inclusion problem of Langevin equation with two different fractional orders,” Advances In Difference Equations, 2012.
- Ming Li, and Wei Zhao, “On Noise,” Mathematical Problems in Engineering, vol. 2012, pp. 1–23, 2012.
- Guotao Wang, Lihong Zhang, and Guangxing Song, “Boundary value problem of a nonlinear Langevin equation with two different fractional orders and impulses,” Fixed Point Theory and Applications, 2012.
- Ahmed Alsaedi, Sotiris K. Ntouyas, and Bashir Ahmad, “Existence Results for Langevin Fractional Differential Inclusions Involving Two Fractional Orders with Four-Point Multiterm Fractional Integral Boundary Conditions,” Abstract And Applied Analysis, 2013.
- Jing Zhao, Peifen Lu, and Yiliang Liu, “Existence and Numerical Simulation of Solutions for Fractional Equations Involving Two Fractional Orders with Nonlocal Boundary Conditions,” Journal of Applied Mathematics, vol. 2013, pp. 1–15, 2013.
- Yiliang Liu, and Liang Lu, “A Class of Fractional -Laplacian Integrodifferential Equations in Banach Spaces,” Abstract and Applied Analysis, vol. 2013, pp. 1–9, 2013.
- Tao Yu, Ke Deng, and Maokang Luo, “Existence and uniqueness of solutions of initial value problems for nonlinear langevin equation involving two fractional orders,” Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 6, pp. 1661–1668, 2014.
- Bashir Ahmad, Juan J. Nieto, Ahmed Alsaedi, and Hana Al-Hutami, “Existence of solutions for nonlinear fractional q-difference integral equations with two fractional orders and nonlocal four-point boundary conditions,” Journal of The Franklin Institute-Engineering and Applied Mathematics, vol. 351, no. 5, pp. 2890–2909, 2014.
- Ivan Area, Eduardo Godoy, and Juan J. Nieto, “Fixed point theory approach to boundary value problems for second-order difference equations on non-uniform lattices,” Advances in Difference Equations, 2014.