eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2016-08-09 4 3 60 66 10.12691/tjant-4-3-2 TJANT2016432 article Rabha W. Ibrahim 1 Adem K?l??man akilic@upm.edu.my 2 Faten H. Damag 2 Institute of Mathematical Sciences, University Malaya, Malaysia Department of Mathematics, University Putra Malaysia, Serdange, Malaysia This paper highlights the mathematical model of biological experiments, that have an effect on our lives. We suggest a mathematical model involving fractional differential operator, kind of hybrid iterative fractional differential equations. Our technique is based on monotonous iterative in the nonlinear analysis. The monotonous sequences described extremal solutions converging for hybrid monotonous fractional iterative differential equations. We apply the monotonous iterative method under appropriate conditions to prove the existence of extreme solutions. The tool relies on the Dhage fixed point Theorem. This theorem is required in biological studies in which increasing or decreasing know freshly split bacterial and could control. http://pubs.sciepub.com/tjant/4/3/2/tjant-4-3-2.pdf fractional differential equation fractional differential operator fractional calculus monotonous sequences extreme solution