New iterative method: An application for solving fractional physical differential equations

Abstract and Applied Analysis

Volumn 2013, Issue , 2013, Pages

  Hemeda, A A ^a  

^a Tanta University   (Egypt)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84878689795     PISSN: 10853375     EISSN: 16870409     Source Type: Journal    
DOI: 10.1155/2013/617010     Document Type: Article

References (29)

1. Miller K., Ross B., An Introduction to the Fractional Calculus and Fractional Diffrential Equations 1993 New York, NY, USA John Wiley & Sons
2. Oldham K. B., Spanier J., The Fractional Calculus 1974 London, UK Academic Press MR0361633 ZBL0292.26011
3. Podlubny I., Fractional Differential Equations 1999 198 San Diego, Calif, USA Academic Press MR1658022 ZBL1056.93542
4. Amairi M., Aoun M., Najar S., Abdelkrim M. N., A constant enclosure method for validating existence and uniqueness of the solution of an initial value problem for a fractional differential equation. Applied Mathematics and Computation 2010 217 5 2162 2168 10.1016/j.amc.2010.07.015 MR2727962 ZBL1250.34006
5. Deng J., Ma L., Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations. Applied Mathematics Letters 2010 23 6 676 680 10.1016/j.aml.2010.02.007 MR2609797 ZBL1201.34008
6. Girejko E., Mozyrska D., Wyrwas M., A sufficient condition of viability for fractional differential equations with the Caputo derivative. Journal of Mathematical Analysis and Applications 2011 381 1 146 154 10.1016/j.jmaa.2011. 04.004 MR2796198 ZBL1222.34007
7. Ray S. S., Bera R. K., Solution of an extraordinary differential equation by Adomian decomposition method. Journal of Applied Mathematics 2004 4 331 338 10.1155/S1110757X04311010 MR2100259 ZBL1080.65069 (Pubitemid 40809689)
8. Dehghan M., Manafian J., Saadatmandi A., Solving nonlinear fractional partial differential equations using the homotopy analysis method. Numerical Methods for Partial Differential Equations 2010 26 2 448 479 10.1002/num.20460 MR2605472 ZBL1185.65187
9. Hashim I., Abdulaziz O., Momani S., Homotopy analysis method for fractional IVPs. Communications in Nonlinear Science and Numerical Simulation 2009 14 3 674 684 10.1016/j.cnsns.2007.09.014 MR2449879 ZBL1221.65277
10. Odibat Z., Momani S., Xu H., A reliable algorithm of homotopy analysis method for solving nonlinear fractional differential equations. Applied Mathematical Modelling 2010 34 3 593 600 10.1016/j.apm.2009.06.025 MR2563341 ZBL1185.65139
11. Hemeda A. A., Homotopy perturbation method for solving partial differential equations of fractional order. International Journal of Mathematical Analysis 2012 6 49-52 2431 2448 MR2966013
12. Hemeda A. A., Homotopy perturbation method for solving systems of nonlinear coupled equations. Applied Mathematical Sciences 2012 6 93-96 4787 4800 MR2950641
13. Esmaeili S., Shamsi M., Luchko Y., Numerical solution of fractional differential equations with a collocation method based on Müntz polynomials. Computers & Mathematics with Applications 2011 62 3 918 929 10.1016/j.camwa.2011.04.023 MR2824680 ZBL1228.65132
14. Hemeda A. A., Variational iteration method for solving wave equation. Computers & Mathematics with Applications 2008 56 8 1948 1953 10.1016/j.camwa.2008.04.010 MR2466697 ZBL1165.65396
15. Hemeda A. A., Variational iteration method for solving non-linear partial differential equations. Chaos, Solitons and Fractals 2009 39 3 1297 1303 10.1016/j.chaos.2007.06.025 MR2512934 ZBL1197.35227
16. Hemeda A. A., Variational iteration method for solving nonlinear coupled equations in 2-dimensional space in fluid mechanics. International Journal of Contemporary Mathematical Sciences 2012 7 37-40 1839 1852 MR2958998 ZBL1254.76110
17. Sakar M. G., Erdogan F., Yldrm A., Variational iteration method for the time-fractional Fornberg-Whitham equation. Computers & Mathematics with Applications 2012 63 9 1382 1388 10.1016/j.camwa.2012.01.031 MR2912063 ZBL1247.65138
18. Doha E. H., Bhrawy A. H., Ezz-Eldien S. S., Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations. Applied Mathematical Modelling 2011 35 12 5662 5672 10.1016/j.apm.2011.05.011 MR2820942 ZBL1228.65126
19. Doha E. H., Bhrawy A. H., Ezz-Eldien S. S., A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order. Computers & Mathematics with Applications 2011 62 5 2364 2373 10.1016/j.camwa.2011.07.024 MR2831698 ZBL1231.65126
20. Daftardar-Gejji V., Jafari H., An iterative method for solving nonlinear functional equations. Journal of Mathematical Analysis and Applications 2006 316 2 753 763 10.1016/j.jmaa.2005.05.009 MR2207344 ZBL1087.65055 (Pubitemid 43033583)
21. Hemeda A. A., New iterative method: application to nth-order integro-differential equations. International Mathematical Forum 2012 7 47 2317 2332
22. Hemeda A. A., Formulation and solution of n th-order derivative fuzzy integrodifferential equation using new iterative method with a reliable algorithm. Journal of Applied Mathematics 2012 2012 17 10.1155/2012/325473 325473 MR2979467 ZBL1251.34015
23. Saadatmandi A., Dehghan M., A new operational matrix for solving fractional-order differential equations. Computers & Mathematics with Applications 2010 59 3 1326 1336 10.1016/j.camwa.2009.07.006 MR2579495 ZBL1189.65151
24. Doha E. H., Bhrawy A. H., Ezz-Eldien S. S., A new Jacobi operational matrix: an application for solving fractional differential equations. Applied Mathematical Modelling 2012 36 10 4931 4943 10.1016/j.apm.2011.12.031
25. Ghazanfari B., Ghazanfari A. G., Fuladvand M., Modification of the homotopy perturbation method for numerical solution of nonlinear wave and system of nonlinear wave equations. The Journal of Mathematics and Computer Science 2011 3 2 212 224
26. Caputo M., Linear methods of dissipation whose Q is almost frequency independent, part II. Journal of the Royal Society of Medicine 1967 13 529 539
27. Cherruault Y., Convergence of Adomian's method. Kybernetes 1989 18 2 31 38 10.1108/eb005812 MR1009979 ZBL0697.65051
28. Jerri A. J., Introduction to Integral Equations with Applications 1999 2nd New York, NY, USA Wiley-Interscience MR1800272
29. Bhalekar S., Daftardar-Gejji V., Convergence of the new iterative method. International Journal of Differential Equations 2011 2011 10 989065 MR2854946 ZBL1239.34014