## THERMAL SCIENCE

International Scientific Journal

### LOCAL FRACTIONAL EULER'S METHOD FOR THE STEADY HEAT-CONDUCTION PROBLEM

**ABSTRACT**

In this paper, the local fractional Euler's method is proposed to consider the steady heat-conduction problem for the first time. The numerical solution for the local fractional heat-relaxation equation is presented. The comparison between numerical and exact solutions is discussed.

**KEYWORDS**

PAPER SUBMITTED: 2015-12-21

PAPER REVISED: 2016-01-05

PAPER ACCEPTED: 2016-01-28

PUBLISHED ONLINE: 2016-09-24

**THERMAL SCIENCE** YEAR

**2016**, VOLUME

**20**, ISSUE

**Supplement 3**, PAGES [S735 - S738]

- Yang, X. J., et al., Local Fractional Integral Transforms and their Applications, Academic Press, New York, USA, 2015
- Zhang, Y., et al., An Efficient Analytical Method for Solving Local Fractional Nonlinear PDEs Arising in Mathematical Physics, Applied Mathematical Modelling, 40 (2016), 3, pp. 1793-1799
- Zhao, D., et al., On the Fractal Heat-Transfer Problems with Local Fractional Calculus, Thermal Science, 19 (2015), 5, pp. 1867-1871
- Yang, X. J., et al., Local Fractional Similarity Solution for the Diffusion Equation Defined on Cantor Sets, Applied Mathematical Letters, 47 (2015), Sep., pp. 54-60
- Jafari, H., et al., A Decomposition Method for Solving Diffusion Equations via Local Fractional Time Derivative, Thermal Science, 19 (2015), Suppl. 1, pp. S123-S129
- Yang, X. J., et al., A New Numerical Technique for Solving the Local Fractional Diffusion Equation: Two-Dimensional Extended Differential Transform Approach, Applied Mathematics and Computation, 274 (2016), Feb., pp. 143-151
- Zhang, Y., et al., Local Fractional Variational Iteration Algorithm II for Non-Homogeneous Model Associated with the Non-Differentiable Heat Flow, Advances in Mechanical Engineering, 7 (2015), 10, pp. 1-7
- Sarikaya, M. Z., et al., On Generalized some Integral Inequalities for Local Fractional Integrals, Applied Mathematics and Computation, 276 (2016), Mar., pp. 316-323
- Yang, X. J., Advanced Local Fractional Calculus and its Applications, World Science, New York, USA, 2012
- Wang, Y., et al., Solving Fractal Steady Heat-Transfer Problems with the Local Fractional Sumudu Transform, Thermal Science, 19 (2015), Suppl. 2, pp. S637-S641
- Yang, X. J., et al., An Asymptotic Perturbation Solution for a Linear Oscillator of Free Damped Vibrations in Fractal Medium Described by Local Fractional Derivatives, Communications in Nonlinear Science and Numerical Simulation, 29 (2015), 1, pp. 499-504
- Erden, S., et al., Generalized Pompeiu Type Inequalities for Local Fractional Integrals and its Applications, Applied Mathematics and Computation, 274 (2016), Feb., pp. 282-291
- Robinson, J. C., An Introduction to Ordinary Differential Equations, Cambridge University Press, Cambridge, UK, 2004