Approximate controllability of fractional order semilinear systems with bounded delay

By Surendra Kumar, Nagarajan Sukavanam. 2012

214 citations recorded by the source corpus.

Abstract In this paper, sufficient conditions are established for the approximate controllability of a class of semilinear delay control systems of fractional order. The existence and uniqueness of mild solution of the system is also proved. The results are obtained by using contraction principle and the Schauder fixed point theorem. Some examples are given to illustrate the theory.

Subfields: Applied Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/a9bf4eb92079c239280d731fa530ccffaf7c6d73

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In Applied Mathematics

In Control and Systems Engineering

In Numerical Analysis

Citations in the corpus

Controllability of Nonlocal Fractional Differential Systems of Order α ∈ (1,2] In Banach Spaces (2013, background): “Kumar and Sukavanam [12] established sufficient conditions for approximate controllability of a class of semilinear delay control systems of fractional order.”
Approximate controllability of fractional stochastic differential inclusions with nonlocal conditions (2016, background): “(26) Approximate controllability of fractional order systems has been reported in the papers (27,28,29,30,31,26).”
Approximate Controllability of Fractional Sobolev-Type Evolution Equations in Banach Spaces (2013, background): “[15–21], Kumar and Sukavanam [22], Li and Yong [37], Dauer and Mahmudov [28], Mahmudov [27, 29], and the references therein.”
Approximate controllability for fractional differential equations of sobolev type via properties on resolvent operators (2017, background): “2), which has been studied by several authors, see for instance [5, 13, 20, 30] and the references therein.”
Approximate Controllability of Fractional Semilinear Stochastic System of Order α∈ (1,2] (2016, background): “Using existence results for mild solutions, in [14, 17, 18] authors established sufficient conditions for the approximate controllability of a class of fractional order semilinear deterministic systems.”
Controllability of Sobolev type fractional evolution systems (2014, background): “For more interesting theory results and scientific applications of fractional differential equations, we cite the monographs [2, 3, 4, 5, 6], the research papers [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31] and the references therein.”