Existence And Controllability Results For Fractional Control Systems In Reflexive Banach Spaces Using Fixed Point Theorem

Main Article Content

Naseif Jasim AL-Jawari

Abstract

       In this paper, a fixed point theorem of nonexpansive mapping is established to study the existence and sufficient conditions for the controllability of nonlinear fractional control systems in reflexive Banach spaces. The result so obtained have been modified and developed in arbitrary space having Opial’s condition by using fixed point theorem deals with nonexpansive mapping defined on a set has normal structure. An application is provided to show the effectiveness of the obtained result.

Downloads

Download data is not yet available.

Article Details

How to Cite
1.
AL-Jawari NJ. Existence And Controllability Results For Fractional Control Systems In Reflexive Banach Spaces Using Fixed Point Theorem. Baghdad Sci.J [Internet]. 2020Dec.1 [cited 2021Jan.25];17(4):1283. Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/4531
Section
article

References

Balachandran K, Kokila J. Controllability of Nonlinear Implicit Fractional Dynamic Systems. IMA J Appl Math. 2014; 79: 562-570.

AL-Jawari, N J, Shaker S M. Controllability of Fractional Control Systems Using Schauder Fixed Point Theorem. AJBAS. 2016; 10(8):25-30.

Li Ding X, Nieto J. Controllability of Nonlinear Fractional Delay Dynamical Systems with Prescribed Controls. Nonlinear Analysis: Modeling and control. 2018; 23(1): 1-18.

Lizzy R M, Balachandran K. Boundary Controllab-ility of Nonlinear Stochastic Fractional Systems in Hilbert Spaces. Int. J. Appl. Math. Comput. Sci. 2018; 28(1):123-133.

Mater M H. On Controllability of Linear and Nonlinear Fractional Integrodifferential System. FDC. 2019; 9(1): 19-32.

Nawaz M, Wei J, Sheng J, Niazi A, Yang L. On The Controllability of Nonlinear Fractional System with Control Delay. Hacet. J. Math. Stat. 2020; 49(1): 294-302.

Limaye B V. Functional Analysis, Second Edition, New Age International (p) Ltd., Publishers: New Delhi, Mumbai; 1996.

Denkowski Z, Migorski S, Papageorgiou N. An Introduction to Nonlinear Analysis: Applications. Kluwer Academic Publishers: NewYork, London; 2003.

Moosaei M. Fixed Points and Common Fixed Points for Fundamentally Nonexpansive Mappings on Banach spaces. J. hyperstructures. 2015;4(1): 50-56.

Dozo, E L. Multivalued Nonexpansive Mappings and Opial’s Condition. Amer. Math. Soc. 1973; 38(2); 286-292.

Radhakrishnan, M, Rajesh S, Agrawal S. Some Fixed Point Theorem on Non-Convex Sets, Appl. Gen. Topol. 2017; 18(2): 377-390.

Kilbas A, Srivastava H, Trujillo J. Theory and Applications of Fractional Differential Equations. Elsevier: Amsterdam; 2006.