A reproducing kernel method for solving nonlocal fractional boundary value problems

Applied Mathematics Letters

Volumn 25, Issue 5, 2012, Pages 818-823

  Geng, Fazhan ^a   Cui, Minggen ^b  

^a CHANGSHU INSTITUTE OF TECHNOLOGY   (China)

^b HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Fractional differential equations; Nonlocal boundary value problems; Reproducing kernel method; Series solutions

Indexed keywords

FRACTIONAL DIFFERENTIAL EQUATIONS; INTEGER ORDER; NONLOCAL; NONLOCAL BOUNDARY-VALUE PROBLEMS; NONSINGULAR; NUMERICAL EXAMPLE; REPRODUCING KERNEL; REPRODUCING KERNEL METHOD; SERIES SOLUTIONS;

MATHEMATICAL TECHNIQUES;

BOUNDARY VALUE PROBLEMS;

EID: 84857047498     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2011.10.025     Document Type: Article

References (21)

1. S.G. Samko, A.A. Kilbas, and O.I. Marichev Fractional Integral and Derivatives, Theory and Applications 1993 Gordon and Breach Switzerland
2. A.A. Kilbas, and S. Marzan Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions Differ. Equ. 1141 2005 84 89 (Pubitemid 40551100)
3. I. Podlubny Fractional Differential Equations 1999 Academic Press San Diego
4. V. Lakshmikantham, and A.S. Vatsala Theory of fractional differential inequalities and applications Commun. Appl. Anal. 11 2007 395 402
5. V. Lakshmikantham, and A.S. Vatsala Basic theory of fractional differential equations Nonlinear Anal. TMA 698 2008 2677 2683
6. A. Ghorbani Toward a new analytical method for solving nonlinear fractional differential equations Comput. Methods Appl. Mech. Engrg. 197 2008 4173 4179
7. Y.Z. Hu, Y. Luo, and Z.Y. Lu Analytical solution of the linear fractional differential equation by Adomian decomposition method J. Comput. Appl. Math. 215 2008 220 229 (Pubitemid 351318114)
8. A.M.A. El-Sayed, I.L. El-Kalla, and E.A.A. Ziada Analytical and numerical solutions of multi-term nonlinear fractional orders differential equations Appl. Numer. Math. 60 2010 788 797
9. Z. Bai On positive solutions of a nonlocal fractional boundary value problem Nonlinear Anal. 72 2010 916 924
10. H.A.H. Salem On the fractional order m-point boundary value problem in reflexive Banach spaces and weak topologies J. Comput. Appl. Math. 224 2009 565 572
11. W. Zhong, and W. Lin Nonlocal and multiple-point boundary value problem for fractional differential equations Comput. Math. Appl. 59 2010 1345 1351
12. M. Ur Rehman, and R.A. Khan Existence and uniqueness of solutions for multi-point boundary value problems for fractional differential equations Appl. Math. Lett. 23 2010 1038 1044
13. B. Ahmad, and S. Sivasundaram On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order Appl. Math. Comput. 217 2010 480 487
14. M.G. Cui, and Y.Z. Lin Nonlinear Numerical Analysis in Reproducing Kernel Space 2009 Nova Science Pub. Inc.
15. A. Berlinet, and C. Thomas-Agnan Reproducing Kernel Hilbert Space in Probability and Statistics 2004 Kluwer Academic Publishers
16. F.Z. Geng, and M.G. Cui Solving singular nonlinear second-order periodic boundary value problems in the reproducing kernel space Appl. Math. Comput. 192 2007 389 398
17. F.Z. Geng, and M.G. Cui Solving a nonlinear system of second order boundary value problems J. Math. Anal. Appl. 327 2007 1167 1181
18. F.Z. Geng Solving singular second order three-point boundary value problems using reproducing kernel Hilbert space method Appl. Math. Comput. 215 2009 2095 2102
19. X.Y. Li, and B.Y. Wu Reproducing kernel method for singular fourth order four-point boundary value problems Bull. Malays. Math. Sci. Soc. 34 2011 147 151
20. P. Bouboulis, and M. Mavroforakis Reproducing kernel Hilbert Spaces and fractal interpolation J. Comput. Appl. Math. 235 2011 3425 3434
21. M. Mohammadi, and R. Mokhtari Solving the generalized regularized long wave equation on the basis of a reproducing kernel space J. Comput. Appl. Math. 235 2011 4003 4014