A reproducing kernel Hilbert space method for solving systems of fractional integrodifferential equations

Abstract and Applied Analysis

Volumn 2014, Issue , 2014, Pages

  Bushnaq, Samia ^a   Maayah, Banan ^b   Momani, Shaher ^b,c   Alsaedi, Ahmed ^c  

^a PRINCESS SUMAYA UNIVERSITY FOR TECHNOLOGY   (Jordan)

^b UNIVERSITY OF JORDAN   (Jordan)

^c KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84899461005     PISSN: 10853375     EISSN: 16870409     Source Type: Journal    
DOI: 10.1155/2014/103016     Document Type: Article

References (21)

1. Podlubuy I., Fractional Differential Equations 1999 New York, NY, USA Academic Press MR1658022
2. Mainardi F., Carpinteri A., Mainardi F., Fractional calculus: some basic problems in continuum and statistical mechanics. Fractals and Fractional Calculus in Continuum Mechanics 1997 New York, NY, USA Springer MR1611587
3. Ertürk V. S., Momani S., Solving systems of fractional differential equations using differential transform method. Journal of Computational and Applied Mathematics 2008 215 1 142 151 10.1016/j.cam.2007.03.029 MR2400624 ZBL1141.65088 (Pubitemid 351318110)
4. Duan J., An J., Xu M., Solution of system of fractional differential equations by Adomian decomposition method. Applied Mathematics 2007 22 1 7 12 10.1007/s11766-007-0002-2 MR2298706 ZBL1125.26008
5. Mohamed A. S., Mahmoud R. A., An algorithm for the numerical solution of systems of fractional differential equations. International Journal of Computer Applications 2013 65 11 10.5120/10970-6105
6. Momani S., Qaralleh R., An efficient method for solving systems of fractional integro-differential equations. Computers & Mathematics with Applications 2006 52 3-4 459 470 10.1016/j.camwa.2006.02.011 MR2263514 ZBL1137.65072 (Pubitemid 44648715)
7. Zurigat M., Momani S., Alawneh A., Homotopy analysis method for systems of fractional integro-differential equations. Proceeding of the 4th International Workshop of Advanced Computation for Engineering Applications 2008 106 111
8. Zurigat M., Momani S., Odibat Z., Alawneh A., The homotopy analysis method for handling systems of fractional differential equations. Applied Mathematical Modelling 2010 34 1 24 35 10.1016/j.apm.2009.03.024 MR2566678 ZBL1185.65140
9. Momani S., Odibat Z., Numerical approach to differential equations of fractional order. Journal of Computational and Applied Mathematics 2007 207 1 96 110 10.1016/j.cam.2006.07.015 MR2332951 ZBL1119.65127 (Pubitemid 46935390)
10. Abdulaziz O., Hashim I., Momani S., Solving systems of fractional differential equations by homotopy-perturbation method. Physics Letters A: General, Atomic and Solid State Physics 2008 372 4 451 459 2-s2.0-37549050173 10.1016/j.physleta.2007.07.059 ZBL1217.81080
11. Lin Y., Zhou Y., Solving nonlinear pseudoparabolic equations with nonlocal boundary conditions in reproducing kernel space. Numerical Algorithms 2009 52 2 173 186 10.1007/s11075-009-9263-6 MR2563700 ZBL1180.65129
12. Ghazanfari B., Ghazanfari A. G., Solving system of fractional differential equations by fractional complex transform method. Asian Journal of Applied Sciences 2012 5 6 438 444 10.3923/ajaps.2012.438.444
13. Saeed R. K., Sadeq H. M., Solving a system of linear fredholm fractional integro-differential equations using homotopy perturbation method. Australian Journal of Basic and Applied Sciences 2010 4 4 633 638 2-s2.0-77953000182
14. Bushnaq S., Momani S., Zhon Y., A reproducing Kernel Hilbert space method for solving integro-differential equations of fractional order. Journal of Optimization Theory and Applications 2012 156 1 96 105 10.1007/s10957-012-0207-2
15. Cui M., Lin Y., Nonlinear Numerical Analysis in the Reproducing Kernel Hilbert Space 2009 New York, NY, USA Nova Science Publishers MR2502102
16. Leszczynski J. S., An Introduction to Fractional Mechanics 2011 Czestochowa, Poland Czestochowa University of Technology
17. Caputo M., Linear Models of Dissipation whose Q is almost Frequency Independent-II. Geophysical Journal of the Royal Astronomical Society 1967 13 5 529 539 10.1111/j.1365-246X.1967.tb02303.x
18. Kilbas A. A., Srivastava H. M., Trujillo J. J., Theory and Applications of Fractional Differential Equations 2006 Amsterdam, The Netherlands Elsevier MR2218073
19. Hilfer R., Applications of Fractional Calculus in Physics 2000 River Edge, NJ, USA World Scientific 10.1142/9789812817747 MR1890104
20. Samko S. G., Kilbas A. A., Marichev O. I., Fractional Integral and Derivatives: Theory and Applications 1993 Yverdon, Switzerland Gordon and Breach Science Publishers MR1347689
21. Li C.-l., Cui M.-G., The exact solution for solving a class nonlinear operator equations in the reproducing kernel space. Applied Mathematics and Computation 2003 143 2-3 393 399 10.1016/S0096-3003(02)00370-3 MR1981704 ZBL1034.47030