- 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
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 325984, 15 pages
On Antiperiodic Boundary Value Problems for Higher-Order Fractional Differential Equations
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Received 18 May 2012; Accepted 1 July 2012
Academic Editor: Dumitru Baleanu
Copyright © 2012 Ahmed Alsaedi 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. Podlubny, Fractional Differential Equations, Academic Press, San Diego, Calif, USA, 1999.
- G. M. Zaslavsky, Hamiltonian Chaos and Fractional Dynamics, Oxford University Press, Oxford, UK, 2005.
- R. L. Magin, Fractional Calculus in Bioengineering, Begell House Publisher, Connecticut, Conn, USA, 2006.
- 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.
- J. Sabatier, O. P. Agrawal, and J. A. T. Machado, Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, Dordrecht, The Netherlands, 2007.
- D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional calculus models and numerical methods. Series on Complexity, Nonlinearity and Chaos, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, USA, 2012.
- M. P. Lazarevic and A. M. Spasic, “Finite-time stability analysis of fractional order time-delay systems: Gronwall's approach,” Mathematical and Computer Modelling, vol. 49, no. 3-4, pp. 475–481, 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.
- R. P. Agarwal, M. Belmekki, and M. Benchohra, “A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative,” Advances in Difference Equations, vol. 2009, Article ID 981728, 47 pages, 2009.
- V. Gafiychuk and B. Datsko, “Mathematical modeling of different types of instabilities in time fractional reaction-diffusion systems,” Computers & Mathematics with Applications, vol. 59, no. 3, pp. 1101–1107, 2010.
- R. P. Agarwal, V. Lakshmikantham, and J. J. Nieto, “On the concept of solution for fractional differential equations with uncertainty,” Nonlinear Analysis. Theory, Methods & Applications, vol. 72, no. 6, pp. 2859–2862, 2010.
- B. Ahmad, “Existence of solutions for irregular boundary value problems of nonlinear fractional differential equations,” Applied Mathematics Letters, vol. 23, no. 4, pp. 390–394, 2010.
- J. J. Nieto, “Maximum principles for fractional differential equations derived from Mittag-Leffler functions,” Applied Mathematics Letters, vol. 23, no. 10, pp. 1248–1251, 2010.
- D. Baleanu, O. G. Mustafa, and R. P. Agarwal, “An existence result for a superlinear fractional differential equation,” Applied Mathematics Letters, vol. 23, no. 9, pp. 1129–1132, 2010.
- E. Hernandez, D. O'Regan, and K. Balachandran, “On recent developments in the theory of abstract differential equations with fractional derivatives,” Nonlinear Analysis. Theory, Methods & Applications, vol. 73, no. 10, pp. 3462–3471, 2010.
- D. Baleanu, O. G. Mustafa, and D. O'Regan, “A Nagumo-like uniqueness theorem for fractional differential equations,” Journal of Physics A, vol. 44, no. 39, Article ID 392003, 6 pages, 2011.
- B. Ahmad and J. J. Nieto, “Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions,” Boundary Value Problems, vol. 2011, p. 36, 2011.
- B. Ahmad, J. J. Nieto, A. Alsaedi, and M. 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.
- G. Wang, D. Baleanu, and L. Zhang, “Monotone iterative method for a class of nonlinear fractional differential equations,” Fractional Calculus and Applied Analysis, vol. 15, no. 2, pp. 244–252, 2012.
- A. Aghajani, Y. Jalilian, and J. J. Trujillo, “On the existence of solutions of fractional integro-differential equations,” Fractional Calculus and Applied Analysis, vol. 15, no. 1, pp. 44–69, 2012.
- B. Ahmad and J. J. Nieto, “Existence of solutions for anti-periodic boundary value problems involving fractional differential equations via Leray-Schauder degree theory,” Topological Methods in Nonlinear Analysis, vol. 35, no. 2, pp. 295–304, 2010.
- B. Ahmad, “Existence of solutions for fractional differential equations of order with anti-periodic boundary conditions,” Journal of Applied Mathematics and Computing, vol. 34, no. 1-2, pp. 385–391, 2010.
- R. P. Agarwal and B. Ahmad, “Existence theory for anti-periodic boundary value problems of fractional differential equations and inclusions,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1200–1214, 2011.
- B. Ahmad and J. J. Nieto, “Anti-periodic fractional boundary value problems,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1150–1156, 2011.
- G. Wang, B. Ahmad, and L. Zhang, “Impulsive anti-periodic boundary value problem for nonlinear differential equations of fractional order,” Nonlinear Analysis. Theory, Methods & Applications, vol. 74, no. 3, pp. 792–804, 2011.
- J. Cao, Q. Yang, and Z. Huang, “Existence of anti-periodic mild solutions for a class of semilinear fractional differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 1, pp. 277–283, 2012.
- B. Ahmad and J. J. Nieto, “Anti-periodic fractional boundary value problems with nonlinear term depending on lower order derivative,” Fractional Calculus and Applied Analysis, vol. 15, no. 3, pp. 451–462, 2012.
- J. X. Sun, Nonlinear Functional Analysis and its Application, Science Press, Beijing, China, 2008.
- D. R. Smart, Fixed Point Theorems, Cambridge University Press, London, UK, 1980.