Coupled systems of nonlinear fractional differential equations with nonlocal boundary conditions

Panamerican Mathematical Journal

Volumn 19, Issue 3, 2009, Pages 29-39

  Ahmad, Bashir ^a   Graef, John R ^b  

^a KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

^b UNIVERSITY OF TENNESSEE AT CHATTANOOGA   (United States)

Author keywords

Caputo fractional derivative; Coupled system; Existence; Fractional differential equations; Nonlocal boundary conditions; Schauder fixed point theorem

Indexed keywords

EID: 72349091049     PISSN: 10649735     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. C. Bai, J. Fang, The existence of a positive soluation for a singiler coupled system of nonlinear fractional differential equations, Appl. Math. Comput. 150 (2004) 611-621.
2. Z. Bai, H. Lü, Positive solutions for boundary value problems of nonlinear fractional differential equations, J. Math. Anal. Appl. 311 (2005) 495-505. (Pubitemid 41350217)
3. Y. Chen, H. An, Numerical solutions of coupled Burger equations with time and space fractional derivatives, Appl. Math. Comput., in press.
4. K. Deng, Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions, J. Math. Anal. Appl. 179 (1993) 630-637.
5. W. Deng, C. Li, Chaos synchronization of the fractional Lü system, Phys. A 353 (2005) 61-72.
6. K. Diethelm, N. J. Ford, Multi-order fractional differential equations and their numerical solution, Appl. Math. Comput. 154 (2004) 621-640.
7. K. Diethelm, A. D. Freed, On the solution of nonlinear fractional differential equations used in the modeling of viscoplasticity, in: F. Keil, W. Mackens, H. Vob, J. Werther (Eds.), Scientific Computing in Chemical Engineering II: Computational Fluid Dynamics, Reaction Engineering, and Molecular Properties, Springer, Heidelberg, 1999, pp. 217-224.
8. V. Gafiychuk, B. Datsko, V. Meleshko, Mathematical modeling of time fractional reaction-diffusion systems, J. Comput. Appl. Math., in press.
9. V. D. Gejji, Positive solutions of a system of non-autonomous fractional differential equations, J. Math. Anal. Appl. 302 (2005) 56-64.
10. V. D. Gejji, A. Babakhani, Analysis of a system of fractional differential equations, J. Math. Anal. Appl. 293 (2004) 511-522.
11. A. A. Kilbas, H. M. Srivatsava, J. J Trujillo, O. I. Marichev, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.
12. V. Lakshmikantham, S. Leela, J. Vasundhara Devi, Theory of Fractional Dynamic Systems, to be published by Cambridge Academic Publishers, U.K.
13. M. P. Lazarević, Finite time stability analysis of PDα fractional control of robotic time -delay systems, Mech. Res. Comm. 33 (2006) 269-279.
14. K. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993.
15. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
16. S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, 1993.
17. X. Su, Boundary value problem for a coupled system of nonlinear fractional differential equations, Appl. Math. Lett. 22 (2009), 64-69.