## THERMAL SCIENCE

International Scientific Journal

### HE'S FRACTIONAL DERIVATIVE FOR NON-LINEAR FRACTIONAL HEAT TRANSFER EQUATION

**ABSTRACT**

This paper adopts He's fractional derivative for non-linear fractional heat transfer equation. The fractional complex transform and He's variational iteration method are used to solve the fractional equation.

**KEYWORDS**

PAPER SUBMITTED: 2015-12-10

PAPER REVISED: 2016-02-01

PAPER ACCEPTED: 2016-02-01

PUBLISHED ONLINE: 2016-08-13

**THERMAL SCIENCE** YEAR

**2016**, VOLUME

**20**, ISSUE

**3**, PAGES [793 - 796]

- Podlubny, I., Fractional Differential Equations, Academic Press, New York, USA, 1999
- Yang, X. J., Advanced Local Fractional Calculus and its Applications, World Science Publisher, New York, USA, 2012
- Jumarie, G., Modified Riemann-Liouville Derivative and Fractional Taylor Series of Non-Differentiable Functions Further Results, Comp. Math. Appl, 51 (2006), 1, pp. 137-1376
- He, J.-H., A New Fractal Deri vation, Thermal Science, 15 (2011), Suppl. 1, pp. S145-S147
- Fan, J., He, J.-H., Fractal Deriva ive Model for Air Permeability in Hierarchic Porous Media, Abstract and Applied Analysis, 2012 (2012), ID354701
- Fan, J., He, J.-H., Biomimic Design of Multi-Scale Fabric with Efficient Heat Transfer Property, Thermal Science, 16 (2012), 5, pp. 1349-1352
- He, J.-H., A Tutorial Review on Fractal Space Time and Fractional Calculus, Int. J. Theor. Phys, 53 (2014), 11, pp. 3698-3718
- Sayevand, K., Pichaghchi, K., Analysis of Non-Linear Fractional KdV Equation Based on He's Fractional Derivative, Non-Linear Science Letters A., 7 (2016), 3, pp. 77-85
- Liu, F. J., et al., He's Fractional Derivative for Heat Conduction in a Fractal Medium Arising in Silkworm Cocoon Hierarchy, Thermal Science, 19 (2015), 4, pp. 1155-1159
- He, J.-H., Asymptotic Methods for Solitary Solutions and Compactons, Abstract and Applied Analysis, 2012 (2012), ID916793
- He, J.-H., Some Asymptotic Methods for Strongly Nonlinear Equations, Int. J. Mod. Phys. B, 20 (2006), 10, pp. 1141-1199
- Liu, J. F., Modified Variational Iteration Method for Varian Boussinesq Equation, Thermal Science, 19 (2015), 4, pp.1195-1199
- Huang, L. L., Matrix Lagrange Multiplier of the VIM, Journal of Computational Complexity and Applications, 2 (2016), 3, pp. 86-88
- He, J.-H., Li, Z. B., Converting Fractional Differential Equations into Partial Differential Equations, Thermal Science,16 (2012), 2, pp. 331-334
- Abdou, M. A., et al., New Exact Solutions of the Space-Time Fractional Non-Linear Transport Equation in Porous Media, Non-Linear Science Letters, A., 7 (2016), 3, pp. 86-95
- Li, Z. B., et al., Exact Solutions of Time-Fractional Heat Conduc tion Equation by the Fractional Complex Transform, Thermal Science, 16 (2012), 2, pp. 335-338
- Yan, L. M., Modified Homotopy Perturbation Method Coupled with Laplace Transform for Fractional Heat Transfer and Porous Media Equation, Thermal Science, 17 (2013), 5, pp. 1409-1414
- Zhang, M. F., et al., Efficient Homotopy Perturbation Method for Fractional Nonlinear Equations Using Sumudu Transform, Thermal Science, 19 (2015), 4, pp. 1167-1171
- Ma, H. C., et al., Exact Solutions of Nonlinear Fractional Partial Differential Equations by Fractional Sub-Equation Method, Thermal Science, 19 (2015), 4, pp. 1239-1244