International Scientific Journal


In this effort, we propose a new fractional differential operator in the open unit disk. The operator is an extension of the Atangana-Baleanu differential operator without singular kernel. We suggest it for a normalized class of analytic functions in the open unit disk. By employing the extended operator, we study the time-2-D space heat equation and optimizing its solution by a chaotic function.
PAPER REVISED: 2021-02-15
PAPER ACCEPTED: 2021-02-20
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Special issue 2, PAGES [173 - 178]
  1. Li, Zheng-Biao, et al., Exact Solutions of Time-Fractional Heat Conduction Equation by the Fractional Complex Transform, Thermal Science, 16 (2012), 2, pp. 335-338
  2. Ibrahim, R. W., Hamid, A. J., On Two Exact Solutions of Time Fractional Heat Equations Using Different Transforms, Thermal Science, 19 (2015), 1, pp. 43-49
  3. Daras, N. J., Themistocles, M. R., Computational Mathematics and Variational Analysis, Springer, New York, USA, 2020
  4. Kaveh, M., et al., Investigation of Mass Transfer, Thermodynamics, and Greenhouse Gases Properties in Pennyroyal Drying, Journal of Food Process Engineering, 43 (2020), 8, e13446
  5. Atangana, A., Dumitru, B., New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model, Thermal Science, 20 (2016), 2, pp. 763-769
  6. Natiq, H., et al., A New Hyperchaotic Map and Its Application for Image Encryption, The European Physical Journal Plus, 133 (2018), 1, pp. 1-14
  7. MacGregor, T. H., Majorization by Univalent Functions, Duke Mathematical Journal, 34 (1967), 1, pp. 95-102
  8. Ibrahim, R. W., Dumitru, B., Geometric Behavior of a Class of Algebraic Differential Equations in a Complex Domain Using a Majorization Concept, AIMS Mathematic,s 6 (2021), 1, pp. 806-820
  9. Miller, S. S., Petru, T. M., Differential Subordinations: Theory and Applications, CRC Press, Boka Raton, Fla., USA, 2000
  10. Fernandez, A., A Complex Analysis Approach to Atangana-Baleanu Fractional Calculus, Mathematical Methods in the Applied Sciences, 44 (2019), 10, pp. 1-18
  11. Shukla, A. K., Prajapati, J. C., On a Generalization of Mittag-Leffler Function and Its Properties, Journal of Mathematical Analysis and Applications, 336 (2007), 2, pp. 797-811
  12. Haubold, H. J., et al., Mittag-Leffler Functions and Their Applications, Journal of Applied Mathematics, 2011 (2011), pp. 1-52
  13. Godula, J., Vasil'evich, V. S., Sharpness of Certain Campbell and Pommerenke Estimates, Mathematical Notes, 63 (1998), 5, pp. 586-592
  14. Campbell, D. M., Majorization-Subordination Theorems for Locally Univalent Functions, II, Canadian Journal of Mathematics, 25 (1973), 2, pp. 420-425
  15. Goodman, A. W., An Invitation to the Study of Univalent and Multivalent Functions, Intr. Nat. J. Hath. & Mh. Sci., 2 (1979), 2, pp. 163-186

© 2024 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