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Fractional Calculus is a hot topic encompassing a broad list of problems such new analytical and, numerical technique, efficient solution of complex problems in modelling of transient heat and flow problems. In contrast to the well-known integer counterparts, the fractional derivatives and integrals are not local [1-3] widely encountered in applications to transient rheology [4, 5], heat [6, 7] and mass transfer [8, 9], non-linear diffusion in porous and granular media [10], Stefan problem [11-13] manifest this technique as a power tool for efficient engineering solutions of complex problems.
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  1. Oldham , K. B. , Spanier, J., The Fractional Calculus , Academic Press, New York, USA, 1974
  2. Babenko, Yu. I., Heat-Mass Transfer, Methods for Calculation of Thermal and Diffusional Fluxes (in Russian), Khimia Publ., Moscow, 1984
  3. Debnath, L., Nonlinear Partial Differential Equations for Scientist and Engineers, Birkhouser, Boston, USA, 1997
  4. Siddique, I., Vieru, D., Stokes Flows of a Newtonian Fluid with Fractional Derivatives and Slip at the Wall, Int. Rev. Chem. Eng., 3 (2011), 6, pp. 822- 826
  5. Qi, H., Xu, M., Some Unsteady Unidirectional Flows of a Generalized Oldroyd-B Fluid with Fractional Derivative, Appl. Math. Model., 33 (2009), 11, pp. 4184-4191
  6. Agrawal, O. P., Application of Fractional Derivatives in Thermal Analysis of Disk Brakes, Nonlinear Dynamics , 38 (2004), 1-4, pp. 191-206
  7. Kulish , V. V., Lage, J. L. , Fractional-Diffusion Solutions for Transient Local Temperature and Heat Flux, J. Heat Transfer, 122 (2000), 2, pp. 372-376
  8. dos Santos, M. C, et al., Development of Heavy Metal Sorption Isotherm Using Fractional Calculus, Int. Rev. Chem. Eng., 3 (2011), 6, pp. 814-817
  9. Hristov J., Starting Radial Subdiffusion from a Central Point through a Diverging Medium (a Sphere): Heat-Balance Integral Method, Thermal Science, 15 (2011), Suppl. 1, pp. S5-S20
  10. Pfaffenzeller, R. A., Lenzi, M. K., Lenzi, E. K., Modeling of Granular Material Mixing Using Fractional Calculus, Int. Rev. Chem. Eng., 3 (2011), 6, pp. 818-821
  11. Meilanov, R. P., Shabanova, M. R. , Akhmedov, E. N., A Research Note on a Solution of Stefan Problem with Fractional Time and Space Derivatives, Int. Rev. Chem. Eng., 3 (2011), 6, pp. 810-813
  12. Voller, V. R. , An Exact Solution of a Limit Case Stefan Problem Governed by a Fractional Diffusion Equation, Int. J. Heat Mass Transfer, 53 (2010), 23-24, pp. 5622-5625
  13. Liu, J., Xu, M., Some Exact Solutions to Stefan Problems with Fractional Differential Equations, J. Math. Anal. Appl., 351 (2010), 2, pp. 536-542
  14. He, J.-H, Li, Z. B., Converting Fractional Differential Equations into Partial Differential Equations, Thermal Science, 16 (2012), 2, pp. 331-334
  15. Li, Z.-B.,He, J.-H, Zhu, W.-H., Exact Solutions of Time-Fractional Heat Conduction Equation by the Fractional Complex Transform, Thermal Science, 16 (2012), 2, pp. 335-338
  16. Wang, Q.-L., He, J.-H, Li, Z.-B., Fractional Model for Heat Conduction in Polar Bear Hairs, Thermal Science, 16 (2012), 2, pp. 339-342
  17. Siddique, I., Vieru, D., Exact Solutions for Rotational Flow of a Fractional Maxwell Fluid in a Circular Cylinder, Thermal Science, 16 (2012), 2, pp. 345-355
  18. Mahmood, A., On Analytical Study of Factional Oldroyd-B Flow in Annular Region of Two Torsionally Oscillating Cylinders, Thermal Science, 16 (2012), 2, pp. 411-421
  19. Hristov, J., Integral-Balance Solution to the Stokes' First Problem of a Viscoelastic Generalized Second Grade Fluid, Thermal Science, 16 (2012), 2, pp. 395-410
  20. Proti},M. Z., et al., Application of Fractional Calculus in Ground Heat Flux Estimation, Thermal Science, 16 (2012), 2, pp. 373-384 From the Guest Editor of Part One THERMAL SCIENCE: Year 2012, Vol. 16, No. 2, pp. VII-IX IX
  21. Hristov, J., Thermal Impedance at the Interface of Contacting Bodies: 1-D Examples Solved by Semi-Derivatives, Thermal Science, 16 (2012), 2, pp. 623-627
  22. Beibalaev, V. D., Meilanov, R. P., The Dirihlet Problem for the Fractional Poisson's Equation with Caputo Derivatives: A Finite Difference Approximation and a Numerical Solution, Thermal Science, 16 (2012), 2, pp. 385-394
  23. Guo, P., Li, C., Zeng, F., Numerical Simulation of the Fractional Langevin Equation, Thermal Science, 16 (2012), 2, pp. 357-363
  24. Chen, A., Guo, P., Li, C., Numerical Algorithm Based on Fast Convolution for Fractional Calculus, Thermal Science, 16 (2012), 2, pp. 365-371
  25. Wu, L.-Y. He. J.-H., Explosion-Proof Textile with Hierarchical Steiner Tree Structure, Thermal Science, 16 (2012), 2, pp. 343-344
  26. Lorenzo, C. F., Hartley, T. T., Generalized Functions for the Fractional Calculus, NASA/TP- 1999-209424/Revl, 1999

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