- 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 2013 (2013), Article ID 606454, 7 pages
On a New Class of Antiperiodic Fractional Boundary Value Problems
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 9 October 2012; Accepted 6 February 2013
Academic Editor: Ağacık Zafer
Copyright © 2013 Bashir Ahmad 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.
- S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, Switzerland, 1993.
- I. Podlubny, Fractional Differential Equations, vol. 198, Academic Press, San Diego, Calif, USA, 1999.
- 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, Amsterdam, The Netherlands, 2006.
- J. Sabatier, O. P. Agrawal, and J. A. T. Machado, Eds., 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, vol. 3, World Scientific, Boston, Mass, USA, 2012.
- Z. Bai, “On positive solutions of a nonlocal fractional boundary value problem,” Nonlinear Analysis: Theory, Methods and Applications A, vol. 72, no. 2, pp. 916–924, 2010.
- V. Gafiychuk and B. Datsko, “Mathematical modeling of different types of instabilities in time fractional reaction-diffusion systems,” Computers and Mathematics with Applications, vol. 59, no. 3, pp. 1101–1107, 2010.
- D. Băleanu and O. G. Mustafa, “On the global existence of solutions to a class of fractional differential equations,” Computers and Mathematics with Applications, vol. 59, no. 5, pp. 1835–1841, 2010.
- D. Băleanu, 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, no. 36, 9 pages, 2011.
- B. Ahmad and S. K. Ntouyas, “A four-point nonlocal integral boundary value problem for fractional differential equations of arbitrary order,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 2011, no. 22, 15 pages, 2011.
- N. J. Ford and M. L. Morgado, “Fractional boundary value problems: analysis and numerical methods,” Fractional Calculus and Applied Analysis, vol. 14, no. 4, pp. 554–567, 2011.
- 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 S. K. Ntouyas, “A note on fractional differential equations with fractional separated boundary conditions,” Abstract and Applied Analysis, vol. 2012, Article ID 818703, 11 pages, 2012.
- B. Datsko and V. Gafiychuk, “Complex nonlinear dynamics in subdiffusive activator-inhibitor systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 4, pp. 1673–1680, 2012.
- 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.
- 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 q∈ (2,3] 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 of solutions for impulsive anti-periodic boundary value problems of fractional semilinear evolution equations,” Dynamics of Continuous, Discrete and Impulsive Systems A, vol. 18, no. 4, pp. 457–470, 2011.
- B. Ahmad, “New results for boundary value problems of nonlinear fractional differential equations with non-separated boundary conditions,” Acta Mathematica Vietnamica, vol. 36, no. 3, pp. 659–668, 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 and Applications A, vol. 74, no. 3, pp. 792–804, 2011.
- B. Ahmad and J. J. Nieto, “Anti-periodic fractional boundary value problems,” Computers and Mathematics with Applications, vol. 62, no. 3, pp. 1150–1156, 2011.
- Y. Chen, J. J. Nieto, and D. O'Regan, “Anti-periodic solutions for evolution equations associated with maximal monotone mappings,” Applied Mathematics Letters, vol. 24, no. 3, pp. 302–307, 2011.
- 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.
- D. R. Smart, Fixed Point Theorems, Cambridge University Press, Cambridge, UK, 1974.