oa An efficient algorithm on time-fractional partial differential equations with variable coefficients

References

1. Noor MA, Mohyud-Din ST. Modified variational iteration method for heat and wave-like equations. Acta Appl Math. 2008; 104:3:257–269.
   [Google الباحث العلمي]
2. Abbasbandy S. A new application of He's variational iteration method for quadratic Riccati differential equation by using Adomian's polynomials. J Comput Appl Math. 2007; 207:1:59–63.
   [Google الباحث العلمي]
3. Abbasbandy S. Numerical solutions of nonlinear Klein-Gordon equation by variational iteration method. Int J Numer Meth Eng. 2007; 70:7:876–881.
   [Google الباحث العلمي]
4. He JH. Some applications of nonlinear fractional differential equation and their approximations. B Sci Technol Soc. 1999; 15:2:86–90.
   [Google الباحث العلمي]
5. Guo S, Mei L. The fractional variational iteration method using He's polynomials. Phys Lett A. 2011; 375::309–313.
   [Google الباحث العلمي]
6. Guo S, Mei L, Ye F, Qiu Z. Compacton and solitary pattern solutions for nonlinear dispersive KdV-type equations involving Jumarie's fractional derivative. Phys Lett A. 2012; 376::158–164.
   [Google الباحث العلمي]
7. Yang XJ, Baleanu D. Fractal heat conduction problem solved by local fractional variation iteration method. Therm Sci. 2013; 17:2:625–628.
   [Google الباحث العلمي]
8. Baleanu D, Machado JAT, Cattani C, Baleanu MC, Yang XJ. Local fractional variational iteration and decomposition methods for wave equation on Cantor sets within local fractional operators. Abstr Appl Anal. 2013; 2014::6. Article ID 535048.
   [Google الباحث العلمي]
9. Ahmad J, Hassan QM, Mohyud-Din ST. Solitary solutions of the fractional KdV equation using modified Remann-Liouville derivative. J Fract Calc Appl. 2013; 4:2:349–356.
   [Google الباحث العلمي]
10. Zhao Y, Baleanu D, Baleanu MC, Cheng DF, Yang XJ. Mappings for special functions on Cantor sets and special integral transforms via local fractional operators. Abstr Appl Anal. 2013; 2013::6. Article ID 316978.
    [Google الباحث العلمي]
11. Ahmad J, Mohyud-Din ST, Yang XJ. Local fractional decomposition method on wave equation in fractal strings. Mitteilungen Klosterneuburg. 2014; 64:2.
    [Google الباحث العلمي]
12. Yang XJ, Baleanu D, Zhong WP. Approximate solutions for diffusion equations on cantor space-time. Proc Rom Acad A. 2013; 14:2:127–133.
    [Google الباحث العلمي]
13. Momani S, Al-Khaled K. Numerical solution for systems of fractional differential equations by the decomposition method. Appl Math Comput. 2005; 162:3:1351–1365.
    [Google الباحث العلمي]
14. Odibat Z, Momani S. Numerical solution of Fokker-Planck equation with space- and time-fractional derivatives. Phys Lett A. 2007; 369::349–358.
    [Google الباحث العلمي]
15. Ganji Z, Ganji D, Rostamiyan Y. Solitary wave solutions for a time-fraction generalized Hirota-Satsuma coupled KdV equation by an analytical technique. Appl Math Model. 2009; 33::3107–3113.
    [Google الباحث العلمي]
16. Yıldırım A, Koçak H. Homotopy perturbation method for solving the space-time fractional advection-dispersion equation. Adv Water Resour. 2009; 32:12:1711–1716.
    [Google الباحث العلمي]
17. Matinfar M, Saeidy M. Application of homotopy analysis method to fourth order parabolic partial differential equations. Appl Appl Math. 2010; 5:1:70–80.
    [Google الباحث العلمي]
18. Mohyud-Din ST, Noor MA, Waheed A. Variation of parameter method for solving sixth-order boundary value problems. Commun Korean Math Soc. 2009; 24:4:605–615.
    [Google الباحث العلمي]
19. Jang MJ, Chen CL, Liu YC. Two-dimensional differential transform for partial differential equations. Appl Math Comput. 2001; 121::261–270.
    [Google الباحث العلمي]
20. Arikoglu A, Ozkol I. Solution of fractional differential equations by using differential transform method. Chaos, Soliton Fract. 2007; 34:5:1473–1481.
    [Google الباحث العلمي]
21. Zhou JK. Differential transform and its applications for Electrical Circuits. Wuhan, China: Huazhong University Press 1986;. (in Chinese).
    [Google الباحث العلمي]
22. Merdan M, Gokdogan A. Solution of nonlinear oscillators with fractional nonlinearities by using the modified differential transformation method. Math Comput Appl. 2011; 16:3:761–772.
    [Google الباحث العلمي]
23. Kurnaz A, Oturanç G. The differential transforms approximation for the system of ordinary differential equations. Int J Comput Math. 2005; 82:6:709–719.
    [Google الباحث العلمي]
24. Li ZB, He JH. Fractional complex transform for fractional differential equations. Math Comput Appl. 2010; 15:5:970–973.
    [Google الباحث العلمي]
25. Jumarie G. Modified Riemann-Liouville derivative and fractional Taylor series of non-differentiable functions further results. Comput Math Appl. 2006; 51:9-10:1367–1376.
    [Google الباحث العلمي]