THERMAL SCIENCE
International Scientific Journal
EXACT SOLUTIONS OF TIME-FRACTIONAL HEAT CONDUCTION EQUATION BY THE FRACTIONAL COMPLEX TRANSFORM
ABSTRACT
The Fractional Complex Transform is extended to solve exactly time-fractional differential equations with the modified Riemann-Liouville derivative. How to incorporate suitable boundary/initial conditions is also discussed.
KEYWORDS
PAPER SUBMITTED: 2011-05-03
PAPER REVISED: 2011-05-20
PAPER ACCEPTED: 2011-07-11
THERMAL SCIENCE YEAR
2012, VOLUME
16, ISSUE
Issue 2, PAGES [335 - 338]
- Li, Z.B., He, J.H., Fractional Complex Transform for Fractional Differential Equations, Mathematical and Computational Applications, 15(2010), 5, pp. 970-973
- Li, Z.B., An Extended Fractional Complex Transform, Journal of Nonlinear Science and Numerical Simulation, 11(2010), s, pp. 0335-0337
- Jumarie, G., Cauchy's integral formula via the modified Riemann-Liouville derivative for analytic functions of fractional order, Applied Mathematics Letters, 23(2010), 12, pp. 1444-1450
- Jumarie, G., Fractional partial differental equations and modified Riemann- Liouville derivative new methods for solution, Journal of Applied Mathematics and Computing, 24(2007), 1-2, pp. 31-48
- Jumarie, G., modified Riemann-Liouville Derivative and Fractional Taylor series of Non-differentiable Functions Further Results, Computers and Mathematics with Applications, 51 (2006), 9-10, pp. 1367-1376
- Hristov, J., Approximate solutions to fractional subdiffusion equations, European Physical Journal, 193(2011), 1, pp. 229-243
- Hristov, J., Starting radial subdiffusion from a central point through a diverging medium (A sphere): Heat-Balance Integral Method, Thermal Science, 15(2011), pp. S5-S20
- Hristov, J., Heat-balance integral to fractional (half-time) heat diffusion sub-model, Thermal Science, 14(2010), 2, pp. 291-316
- Jafari, H., Kadkhoda, N., Tajadodi, H., et al. Homotopy Perturbation Pade Technique for Solving Fractional Riccati Differential Equations, Int. J. Nonlinear Sci. Num., 11(2010) , pp. 271-275
- Golbabai, A., Sayevand, K., The Homotopy Perturbation Method for Multi-order Time Fractional Differential Equations, Nonlinear Science Letters A, 1(2010),pp.147-154
- He, J. H., Approximate analytical solution for seepage flow with fractional derivatives in porous media, Computer Methods in Applied Mechanics and Engineering, 167(1998), 1-2, pp. 57-68
- Zhang, S., Zhang, H.Q., Fractional sub-equation method and its applications to nonlinear fractional PDEs, Physics Letters A, 375(2011), 7, pp. 1069-1073
- He J.H., Analytical methods for thermal science-An elementary introduction, Thermal Science, 15(2011), s, pp. S1-S3
- He, J.H., A New Fractal Derivation, Thermal Science, 15(2011), s, pp. S145-S147