## THERMAL SCIENCE

International Scientific Journal

### ON LOCAL FRACTIONAL VOLTERRA INTEGRAL EQUATIONS IN FRACTAL HEAT TRANSFER

**ABSTRACT**

In the article, the fractal heat-transfer models are described by the local fractional integral equations. The local fractional linear and nonlinear Volterra integral equations are employed to present the heat transfer problems in fractal media. The local fractional integral equations are derived from the Fourier law in fractal media.

**KEYWORDS**

PAPER SUBMITTED: 2015-12-17

PAPER REVISED: 2016-01-23

PAPER ACCEPTED: 2016-01-26

PUBLISHED ONLINE: 2016-08-14

**THERMAL SCIENCE** YEAR

**2016**, VOLUME

**20**, ISSUE

**Supplement 3**, PAGES [S795 - S800]

- Corduneanu, C., Integral Equations and Applications, Cambridge: Cambridge University Press, 1991
- Deverall, L. I., et al., A New Integral Equation for Heat Flux in Inverse Heat Conduction, ASME Journal of Heat Transfer, 88(1966), pp.327-328
- Frankel, J. I., A Nonlinear Heat Transfer Problem: Solution of Nonlinear, Weakly Singular Volterra Integral Equations of the Second kind, Engineering Analysis with Boundary Elements, 8(1991), 5, 231-238
- Divo, E., et al., A Boundary Integral Equation for Steady Heat Conduction in Anisotropic and Heterogeneous Media, Numerical Heat Transfer B: Fundamentals, 32(1997), pp.37-61
- Tan, Z. M., et al., An Integral Formulation of Transient Radiative Transfer, Journal of Heat Transfer, 123(2001) , 3, pp.466-475
- Kulish, V. V., et al., Integral Equation for the Heat Transfer with the Moving Boundary, Journal of Thermophysics and Heat Transfer, 17(2003), 4, pp.538-540
- Yang, X. J., Baleanu, D., Srivastava, H. M., Local Fractional Integral Transforms and Their Applications, Academic Press, New York, 2015
- Yang, X. J., et al., Nonlinear Dynamics for Local Fractional Burgers' Equation Arising in Fractal Flow, Nonlinear Dynamics, 84(2016), pp.3-7
- Yang, X. J., Srivastava, H. M., 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
- Yang, X. J., et al., Local Fractional Similarity Solution for the Diffusion Equation Defined on Cantor Sets, Applied Mathematical Letters, 47(2015), pp.54-60
- Baleanu, D., et al., Local Fractional Variational Iteration Algorithms for the Parabolic Fokker-Planck Equation Defined on Cantor sets, Progr. Fract. Differ. Appl., 1(2015), 1, pp.1-11
- Cattani, C., Srivastava, H. M., Yang, X. J., Fractional Dynamics, Emerging Science Publishers, 2015
- Yang, X. J., Advanced Local Fractional Calculus and Its Applications, World Science, New York, 2012
- Yang, X. J., et al., Cantor-type Cylindrical-coordinate Method for Differential Equations with Local Fractional Derivatives, Physics Letter A, 377(2013) , 28, pp.1696-1700
- Yang, A. M., et al., A New Coupling Schedule for Series Expansion Method and Sumudu Transform with an Applications to Diffusion Equation in Fractal Heat Transfer, Thermal Science, 19 (2015), Suppl.1, pp.145-149
- Yan, S. P., Local Fractional Laplace Series Expansion Method for Diffusion Equation Arising in Fractal Heat Transfer, Thermal Science, 19(2015), Suppl.1, 131-135
- Yang, X. J., et al., Fractal Heat Conduction Problem Solved by Local Fractional Variation Iteration Method, Thermal Science, 17(2013), 2, pp.625-628
- 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
- Yang, A. M., et al., Laplace Variational Iteration Method for the Two-dimensional Diffusion Equation in Homogeneous Materials, Thermal Science, 19(2015), Suppl.1, pp.163-168
- Yang, X. J., et al., Fractal Boundary Value Problems for Integral and Differential Equations with local Fractional Operators, Thermal Science, 19(2013), 3, pp. 959-966
- Fan, Z. P., et al., Adomian Decomposition Method for Three-dimensional Diffusion Model in Fractal Heat Transfer Involving Local Fractional Derivatives, Thermal Science, 19 (2015), Suppl. 1, pp.137-141
- Jassim, H. K., Local Fractional Laplace Decomposition Method for Nonhomogeneous Heat Equations Arising in Fractal Heat Flow with Local Fractional Derivative, International Journal of Advances in Applied Mathematics and Mechanics, 2 (2015), 4, pp.1-7
- Yang, X. J., et al., Local Fractional Homotopy Perturbation Method for Solving Fractal Partial Differential Equations Arising in Mathematical Physics, Romanian Reports in Physics, 67(2015), 3, pp.752-761
- Zhang, Y., et al., Local Fractional Homotopy Perturbation Method for Solving Non-Homogeneous Heat Conduction Equations in Fractal Domains, Entropy, 17(2015), 10, pp.6753-6764
- Srivastava, H. M., Raina, R. K., Yang, X.-J., Special Functions in Fractional Calculus and Related Fractional Differintegral Equations, World Scientific, Singapore, 2016