Riemann-liouville fractional differential equations with fractional boundary conditions

Fixed Point Theory

Volumn 13, Issue 2, 2012, Pages 329-336

  Ahmad, Bashir ^a   Nieto, Juan J ^a,b  

^a KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

^b UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

Author keywords

Anti periodic boundary conditions; Fixed point theorems; Fractional boundary conditions; Fractional differential equations; Riemann liouville calculus

Indexed keywords

EID: 84870024410     PISSN: 15835022     EISSN: 20669208     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. S. Abbas, M. Benchohra, Existence theory for impulsive partial hyperbolic diferential equations of fractional order at variable times, Fixed Point Theory, 12(2011), 3-16.
2. R.P. Agarwal, B. Andrade, C. Cuevas, Weighted pseudo-almost periodic solutions of a class of semilinear fractional differential equations, Nonlinear Anal. Real World Appl., 11(2010), 3532-3554.
3. R.P. Agarwal, V. Lakshmikantham, J.J. Nieto, On the concept of solution for fractional differential equations with uncertainty, Nonlinear Anal., 72(2010), 2859-2862.
4. B. Ahmad, J.J. Nieto, Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions, Bound. Value Probl., 2009, Art. ID 708576, 11 pp.
5. B. Ahmad, J.J. Nieto, Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions, Comput. Math. Appl., 58(2009), 1838-1843.
6. B. Ahmad, J.J. Nieto, Existence of solutions for anti-periodic boundary value problems involving fractional differential equations via Leray-Schauder degree theory, Topol. Methods Nonlinear Anal., 35(2010), 295-304.
7. Z. Bai, On positive solutions of a nonlocal fractional boundary value problem, Nonlinear Anal., 72(2010), 916-924.
8. M. Belmekki, J.J. Nieto, R. Rodŕiguez-Ĺopez, Existence of periodic solution for a nonlinear fractional differential equation, Bound. Value Probl., (2009), Art. ID 324561, 18 pp.
9. A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204, Elsevier Science B.V., Amsterdam, 2006.
10. J.J. Nieto, Maximum principles for fractional differential equations derived from Mittag-Leffler functions, Appl. Math. Lett., 23(2010), 1248-1251.
11. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
12. J. Sabatier, O.P. Agrawal, J.A.T. Machado (Eds.), Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, Dordrecht, 2007.
13. S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, 1993.
14. D.R. Smart, Fixed Point Theorems, Cambridge University Press, 1980.
15. K. Wang, Y. Li, A note on existence of (anti)-periodic and heteroclinic solutions for a class of second order odes, Nonlinear Anal., 70(2009), 1711-1724.
16. S. Zhang, Positive solutions to singular boundary value problem for nonlinear fractional differential equation, Comput. Math. Appl., 59(2010), 1300-1309.