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Ladde, G. S., Lakshmikantham, V., and Vatsala, A. S. (1985). Monotone iterative techniques for nonlinear differential equations (Vol. 27). Pitman Publishing.

has been cited by the following article:

Article

Extremal Solutions by Monotone Iterative Technique for Hybrid Fractional Differential Equations

1Institute of Mathematical Sciences, University Malaya, Malaysia

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


Turkish Journal of Analysis and Number Theory. 2016, Vol. 4 No. 3, 60-66
DOI: 10.12691/tjant-4-3-2
Copyright © 2016 Science and Education Publishing

Cite this paper:
Rabha W. Ibrahim, Adem Kılıçman, 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.

Correspondence to: Adem  Kılıçman, Department of Mathematics, University Putra Malaysia, Serdange, Malaysia. Email: akilic@upm.edu.my

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.

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