Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions

Computers and Mathematics with Applications

Volumn 58, Issue 9, 2009, Pages 1838-1843

  Ahmad, Bashir ^a   Nieto, Juan J ^b  

^a KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

^b UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

Author keywords

Coupled system; Existence; Fractional differential equations; Schauder fixed point theorem

Indexed keywords

COUPLED SYSTEM; COUPLED SYSTEMS; EXISTENCE; EXISTENCE RESULTS; FRACTIONAL DIFFERENTIAL EQUATIONS; SCHAUDER FIXED POINT THEOREM;

NONLINEAR EQUATIONS; THEOREM PROVING;

BOUNDARY CONDITIONS;

EID: 70349131961     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2009.07.091     Document Type: Article

References (19)

1. Bai Z., and Lü H. Positive solutions for boundary value problems of nonlinear fractional differential equations. J. Math. Anal. Appl. 311 (2005) 495-505
2. Chang Y.K., and Nieto J.J. Some new existence results for fractional differential inclusions with boundary conditions. Math. Comput. Modelling 49 (2009) 605-609
3. Deng W. Numerical algorithm for the time fractional Fokker-Planck equation. J. Comput. Phys. 227 (2007) 1510-1522
4. Ibrahim R.W., and Darus M. Subordination and superordination for univalent solutions for fractional differential equations. J. Math. Anal. Appl. 345 (2008) 871-879
5. Ladaci S., Loiseau J.L., and Charef A. Fractional order adaptive high-gain controllers for a class of linear systems. Commun. Nonlinear Sci. Numer. Simul. 13 (2008) 707-714
6. Rida S.Z., El-Sherbiny H.M., and Arafa A.A.M. On the solution of the fractional nonlinear Schrödinger equation. Phys. Lett. A 372 (2008) 553-558
7. Yang A., and Ge W. Positive solutions for boundary value problems of N-Dimension nonlinear fractional differential system. Bound. Value Probl. 2008 (2008) 15 pages. Article ID 437453
8. Su X., and Zhang S. Solutions to boundary-value problems for nonlinear differential equations of fractional order. Electron. J. Differential Equations 2009 26 (2009) 115
9. Ahmad B., and Nieto J.J. Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions. Bound. Value Probl. 2009 (2009) 11 pages. Article ID 708576
10. Ahmad B., and Nieto J.J. Existence of solutions for nonlocal boundary value problems of higher-order nonlinear fractional differential equations. Abstr. Appl. Anal. 2009 (2009) 9 pages. Article ID 494720
11. Bai C., and Fang J. The existence of a positive solution for a singular coupled system of nonlinear fractional differential equations. Appl. Math. Comput. 150 (2004) 611-621
12. Chen Y., and An H. Numerical solutions of coupled Burgers equations with time and space fractional derivatives. Appl. Math. Comput. 200 (2008) 87-95
13. Gafiychuk V., Datsko B., and Meleshko V. Mathematical modeling of time fractional reaction-diffusion systems. J. Comput. Appl. Math. 220 (2008) 215-225
14. Gejji V.D. Positive solutions of a system of non-autonomous fractional differential equations. J. Math. Anal. Appl. 302 (2005) 56-64
15. α fractional control of robotic time-delay systems. Mech. Res. Comm. 33 (2006) 269-279
16. Su X. Boundary value problem for a coupled system of nonlinear fractional differential equations. Appl. Math. Lett. 22 (2009) 64-69
17. Gafiychuk V., Datsko B., Meleshko V., and Blackmore D. Analysis of the solutions of coupled nonlinear fractional reaction-diffusion equations. Chaos Solitons Fractals 41 (2009) 1095-1104
18. Kilbas A.A., Srivastava H.M., and Trujillo J.J. Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies vol. 204 (2006), Elsevier Science B.V., Amsterdam
19. Podlubny I. Fractional Differential Equations (1999), Academic Press, San Diego