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
Extremal Solutions by Monotone Iterative Technique for Hybrid Fractional Differential Equations
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