# Maximize Minimum Utility Function of Fractional Cloud Computing System Based on Search Algorithm Utilizing the Mittag-Leffler Sum

## Main Article Content

### Abstract

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.

## Article Details

### References

- 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.
- 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.
- R. W. Ibrahim et al., Perturbation of fractional multi-agent systems in cloud entropy computing, Entropy 18 (1) (2016), 31.
- R. W. Ibrahim, A. Gani, Hybrid cloud entropy systems based on Wiener process, Kybernetes 45 (7) (2016), 1072-1083.
- 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.
- 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.
- A. A. Kilbas, H. M. Srivastava and J.J. Trujillo, Theory and applications of fractional differential equations. North-Holland, Mathematics Studies, Elsevier 2006.
- D. Baleanu, J. Machado, and A. Luo, Fractional dynamics and control. Springer Science & Business Media, 2011.
- R. W. Ibrahim, Fractional calculus of Multi-objective functions & Multi-agent systems. Lambert Academic Publishing, Saarbrucken, Germany 2017.
- R. Hilfer, Applications of Fractional Calculus in Physics. Singapore: World Scientific, 2000.
- N. Jafari, et al., Job scheduling in the Expert Cloud based on genetic algorithms, Kybernetes, 43( 8) (2014),1262-1275.
- M. Ashouraie, N. Navimipour, Priority-based task scheduling on heterogeneous resources in the Expert Cloud, Kybernetes: 44 (10) ( 2015), 1455-1471.