THERMAL SCIENCE
International Scientific Journal
SOME NEW APPLICATIONS FOR HEAT AND FLUID FLOWS VIA FRACTIONAL DERIVATIVES WITHOUT SINGULAR KERNEL
ABSTRACT
This paper addresses the mathematical models for the heat-conduction equations and the Navier-Stokes equations via fractional derivatives without singular kernel.
KEYWORDS
PAPER SUBMITTED: 2015-12-28
PAPER REVISED: 2016-01-20
PAPER ACCEPTED: 2016-01-21
PUBLISHED ONLINE: 2016-09-24
THERMAL SCIENCE YEAR
2016, VOLUME
20, ISSUE
Supplement 3, PAGES [S833 - S839]
- Oldham, K. B., Spanier, J., The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order, Academic Press, New York, USA, 1974
- Sabatier, J., et al., Advances in Fractional Calculus, Springer, Dordrecht, The Netherlands, Vol. 4. No. 9, 2007
- Kilbas, A. A., et al., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, The Netherlands, 2006
- Gorenflo, R., Mainardi, F., Fractional Calculus and Stable Probability Distributions, Archives of Mechanics, 50 (1998), 3, pp. 377-388
- Tarasov, V. E., Heat Transfer in Fractal Materials, International Journal of Heat and Mass Transfer, 93 (2016), Feb., pp. 427-430
- Povstenko, Y. Z., Thermoelasticity that Uses Fractional Heat Conduction Equation, Journal of Mathematical Sciences, 162 (2009), 2, pp. 296-305
- Ezzat, M. A., Thermoelectric MHD Non-Newtonian Fluid with Fractional Derivative Heat Transfer, Physics B, 405 (2010), 19, pp. 4188-4194
- Khan, M., et al., Exact Solution for MHD Flow of a Generalized Oldroyd-B Fluid with Modified Darcy's Law, International Journal of Engineering Science, 44 (2006), 5, pp. 333-339
- Caputo, M., Fabrizio, M. A., New Definition of Fractional Derivative without Singular Kernel, Progress in Fractional Differentiation and Applications, 1 (2015), 2, pp. 73-85
- Lozada, J., Nieto, J. J., Properties of a New Fractional Derivative without Singular Kernel, Progress in Fractional Differentiation and Applications, 1 (2015), 1, pp. 87-92
- Alsaedi, A., et al., Fractional Electrical Circuits, Advances in Mechanical Engineering, 7 (2015), 12, pp. 1-7
- Yang, X. J., et al., A New Fractional Derivative without Singular Kernel: Application to the Modelling of the Steady Heat Flow, Thermal Science, 20 (2016), 2, pp. 753-756
- Yang, A. M., et al., On Steady Heat Flow Problem Involving Yang-Srivastava-Machado Fractional Derivative Without Singular Kernel, Thermal Science, 20 (2016), Suppl. 3, pp. S717-S723
- Yang, X. J., Advanced Local Fractional Calculus and Its Applications, World Science, New York, USA, 2012
- ***, Fractional Dynamics (Eds. C. Cattani, H. M. Srivastava, X.-J. Yang), De Gruyter Open, Berlin, 2015, ISBN 978-3-11-029316-6
- Yang, X. J., et al., Local Fractional Integral Transforms and their Applications, Academic Press, New York, USA, 2015
