Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2016, 4(3), 60-66
DOI: 10.12691/tjant-4-3-2
Open AccessArticle

Extremal Solutions by Monotone Iterative Technique for Hybrid Fractional Differential Equations

Rabha W. Ibrahim1, Adem Kılıçman2, and Faten H. Damag2

1Institute of Mathematical Sciences, University Malaya, Malaysia

2Department of Mathematics, University Putra Malaysia, Serdange, Malaysia

Pub. Date: August 09, 2016

Cite this paper:
Rabha W. Ibrahim, Adem Kılıçman and Faten H. Damag. Extremal Solutions by Monotone Iterative Technique for Hybrid Fractional Differential Equations. Turkish Journal of Analysis and Number Theory. 2016; 4(3):60-66. doi: 10.12691/tjant-4-3-2

Abstract

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.

Keywords:
fractional differential equation fractional differential operator fractional calculus monotonous sequences extreme solution

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