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Jordan Y HristovORCID

FROM THE GUEST EDITOR OF PART ONE: FRACTIONAL CALCULUS TO HEAT, MOMENTUM, AND MASS TRANSFER PROBLEMS

ABSTRACT
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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THERMAL SCIENCE YEAR 2012, VOLUME 16, ISSUE No. 2, PAGES [7 - 9]
REFERENCES
[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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From the Guest Editor of Part One: FRACTIONAL CALCULUS TO HEAT, MOMENTUM, AND MASS TRANSFER PROBLEMS

© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence