Title: Maximize Minimum Utility Function of Fractional Cloud Computing System Based on Search Algorithm Utilizing the Mittag-Leffler Sum
Author(s): Rabha W. Ibrahim
Pages: 125-136
Cite as:
Rabha W. Ibrahim, Maximize Minimum Utility Function of Fractional Cloud Computing System Based on Search Algorithm Utilizing the Mittag-Leffler Sum, Int. J. Anal. Appl., 16 (1) (2018), 125-136.


The maximum min utility function (MMUF) problem is an important representative of a large class of cloud computing systems (CCS). Having numerous applications in practice, especially in economy and industry. This paper introduces an effective solution-based search (SBS) algorithm for solving the problem MMUF. First, we suggest a new formula of the utility function in term of the capacity of the cloud. We formulate the capacity in CCS, by using a fractional diffeo-integral equation. This equation usually describes the flow of CCS. The new formula of the utility function is modified recent active utility functions. The suggested technique first creates a high-quality initial solution by eliminating the less promising components, and then develops the quality of the achieved solution by the summation search solution (SSS). This method is considered by the Mittag-Leffler sum as hash functions to determine the position of the agent. Experimental results commonly utilized in the literature demonstrate that the proposed algorithm competes approvingly with the state-of-the-art algorithms both in terms of solution quality and computational efficiency.

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  1. Y. K. Salih et al., A user-centric game selection model based on user preferences for the selection of the best heterogeneous wireless network, Ann. Tlcommun. 70(5-6) (2015), 1–10. Google Scholar

  2. Y. K. Salih et al., An intelligent selection method based on game theory in heterogeneous wireless networks, Trans. Emerg. Telecommun. Technol. 27 (12) (2016), 1641–1652. Google Scholar

  3. R. W. Ibrahim et al., Perturbation of fractional multi-agent systems in cloud entropy computing, Entropy 18 (1) (2016), 31. Google Scholar

  4. R. W. Ibrahim, A. Gani, Hybrid cloud entropy systems based on Wiener process, Kybernetes 45 (7) (2016), 1072–1083. Google Scholar

  5. R. W. Ibrahim, Y. K. Salih, On a fractional multi-agent cloud computing system based on the criteria of the existence of fractional differential equation, Math. Sci. (2017), 1–7. Google Scholar

  6. I. Podlubny, Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Vol. 198. Academic press 1999. Google Scholar

  7. A. A. Kilbas, H. M. Srivastava and J.J. Trujillo, Theory and applications of fractional differential equations. North-Holland, Mathematics Studies, Elsevier 2006. Google Scholar

  8. D. Baleanu, J. Machado, and A. Luo, Fractional dynamics and control. Springer Science & Business Media, 2011. Google Scholar

  9. R. W. Ibrahim, Fractional calculus of Multi-objective functions & Multi-agent systems. Lambert Academic Publishing, Saarbrucken, Germany 2017. Google Scholar

  10. R. Hilfer, Applications of Fractional Calculus in Physics. Singapore: World Scientific, 2000. Google Scholar

  11. N. Jafari, et al., Job scheduling in the Expert Cloud based on genetic algorithms, Kybernetes, 43( 8) (2014),1262-1275. Google Scholar

  12. M. Ashouraie, N. Navimipour, Priority-based task scheduling on heterogeneous resources in the Expert Cloud, Kybernetes: 44 (10) ( 2015), 1455-1471. Google Scholar