Nonlinear fractional integro-differential equations on unbounded domains in a Banach space

Journal of Computational and Applied Mathematics

Volumn 249, Issue , 2013, Pages 51-56

  Zhang, Lihong ^a   Ahmad, Bashir ^b   Wang, Guotao ^a   Agarwal, Ravi P ^b,c  

^a SHANXI NORMAL UNIVERSITY   (China)

^b KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

^c TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Nonlinear fractional integro differential equations Banach space Explicit iterative sequence Error estimate Infinite interval

Indexed keywords

ERROR ESTIMATES; EXPLICIT ITERATIVE; FIXED POINT THEORY; FRACTIONAL INTEGRO-DIFFERENTIAL EQUATION; MONOTONE ITERATIVE TECHNIQUES; SEMI-INFINITE DOMAINS; UNBOUNDED DOMAIN;

BANACH SPACES; DIFFERENTIAL EQUATIONS; ITERATIVE METHODS;

INTEGRODIFFERENTIAL EQUATIONS;

EID: 84875133216     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2013.02.010     Document Type: Article

References (30)

1. I. Podlubny Fractional Differential Equations 1999 Academic Press San Diego
2. A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo Theory and Applications of Fractional Differential Equations North-Holland Mathematics Studies vol. 204 2006 Elsevier Science B.V Amsterdam
3. V. Lakshmikantham, S. Leela, and J.V. Devi Theory of Fractional Dynamic Systems 2009 Cambridge Scientific Publishers Cambridge
4. J. Sabatier, O.P. Agrawal, and J.A.T. Machado Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering 2007 Springer Dordrecht
5. D. Baleanu, K. Diethelm, E. Scalas, and J.J. Trujillo Fractional calculus models and numerical methods Series on Complexity, Nonlinearity and Chaos 2012 World Scientific Boston
6. E. Hernandez, D. O'Regan, and K. Balachandran On recent developments in the theory of abstract differential equations with fractional derivatives Nonlinear Anal. 73 10 2010 3462 3471
7. N.J. Ford, and M.L. Morgado Fractional boundary value problems: analysis and numerical methods Fract. Calc. Appl. Anal. 14 2011 554 567
8. B. Ahmad, and J.J. Nieto Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions Bound. Value Probl. 2011 2011 36 9 pages
9. G. Wang, R.P. Agarwal, and A. Cabada Existence results and the monotone iterative technique for systems of nonlinear fractional differential equations Appl. Math. Lett. 25 2012 1019 1024
10. Z.B. Bai, and W. Sun Existence and multiplicity of positive solutions for singular fractional boundary value problems Comput. Math. Appl. 63 2012 1369 1381
11. R. Sakthivel, N.I. Mahmudov, and J.J. Nieto Controllability for a class of fractional-order neutral evolution control systems Appl. Math. Comput. 218 2012 10334 10340
12. G. Wang, B. Ahmad, and L. Zhang Impulsive anti-periodic boundary value problem for nonlinear differential equations of fractional order Nonlinear Anal. 74 2011 792 804
13. B. Ahmad, and S.K. Ntouyas Existence results for nonlocal boundary value problems for fractional differential equations and inclusions with strip conditions Bound. Value Probl. 2012 2012 55 21 pages
14. R.P. Agarwal, D. O'Regan, and S. Stanek Positive solutions for mixed problems of singular fractional differential equations Math. Nachr. 285 1 2012 27 41
15. A. Arara, M. Benchohra, N. Hamidia, and J.J. Nieto Fractional order differential equations on an unbounded domain Nonlinear Anal. 72 2010 580 586
16. X.K. Zhao, and W.G. Ge Unbounded solutions for a fractional boundary value problem on the infinite interval Acta Appl. Math. 109 2010 495 505
17. S. Liang, and J. Zhang Existence of three positive solutions for m-point boundary value problems for some nonlinear fractional differential equations on an infinite interval Comput. Math. Appl. 61 2011 3343 3354
18. X. Su Solutions to boundary value problem of fractional order on unbounded domains in a Banach space Nonlinear Anal. 74 2011 2844 2852
19. R.P. Agarwal, M. Benchohra, S. Hamani, and S. Pinelas Boundary value problems for differential equations involving Riemann-Liouville fractional derivative on the half-line Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 18 2 2011 235 244
20. S. Liang, and J. Zhang Existence of multiple positive solutions for m-point fractional boundary value problems on an infinite interval Math. Comput. Modelling 54 2011 1334 1346
21. F. Chen, and Y. Zhou Attractivity of fractional functional differential equations Comput. Math. Appl. 62 2011 1359 1369
22. X. Su, and S. Zhang Unbounded solutions to a boundary value problem of fractional order on the half-line Comput. Math. Appl. 61 2011 1079 1087
23. G. Wang, B. Ahmad, and L. Zhang A coupled system of nonlinear fractional differential equations with multi-point fractional boundary conditions on an unbounded domain Abstr. Appl. Anal. 2012 2012 11 pages, Article ID 248709
24. G. Wang Monotone iterative technique for boundary value problems of a nonlinear fractional differential equations with deviating arguments J. Comput. Appl. Math. 236 2012 2425 2430
25. G. Wang, D. Baleanu, and L. Zhang Monotone iterative method for a class of nonlinear fractional differential equations Fract. Calc. Appl. Anal. 15 2012 244 252
26. F.A. McRae Monotone iterative technique and existence results for fractional differential equations Nonlinear Anal. 71 2009 6093 6096
27. J.D. Ramirez, and A.S. Vatsala Monotone iterative technique for fractional differential equations with periodic boundary boundary conditions Opuscula Math. 29 2009 289 304
28. Z. Wei, G. Li, and J. Che Initial value problems for fractional differential equations involving Riemann-Liouville sequential fractional derivative J. Math. Anal. Appl. 367 2010 260 272
29. G.S. Ladde, V. Lakshmikantham, and A.S. Vatsala Monotone Iterative Techniques for Nonlinear Differential Equations 1985 Pitman London
30. Dajun Guo, V. Lakshmikantham, and Xinzhi Liu Nonlinear Integral Equations in Abstract Spaces 1996 Kluwer Academic Publishers