Approximate controllability for fractional differential equations of sobolev type via properties on resolvent operators-Reference-Cited by-同舟云学术

Approximate controllability for fractional differential equations of sobolev type via properties on resolvent operators

Published:2017-08-01 Issue:4 Volume:20 Page:963-987
ISSN:1311-0454
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Chang Yong-Kui¹,Pereira Aldo²,Ponce Rodrigo²

Affiliation:

1. School of Mathematics and Statistics Xidian University , Xi’an 710071 , Shaanxi , China

2. Instituto de Matemática y Física Universidad de Talca Casilla 747 , Talca , Chile

Abstract

Abstract This paper treats the approximate controllability of fractional differential systems of Sobolev type in Banach spaces. We first characterize the properties on the norm continuity and compactness of some resolvent operators (also called solution operators). And then via the obtained properties on resolvent operators and fixed point technique, we give some approximate controllability results for Sobolev type fractional differential systems in the Caputo and Riemann-Liouville fractional derivatives with order 1 < α < 2, respectively. Particularly, the existence or compactness of an operator E −1 is not necessarily needed in our results.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2017-0050/pdf

Reference31 articles.

1. S. Abbas, M. Banerjee, S. Momani, Dynamical analysis of a fractional order modified logistic model. Comp. Math. Appl. 62 (2011), 1098–1104.

2. S. Abbas, M. Benchohra, G.M. N’Guérékata, Topics in Fractional Differential Equations. Springer, New York (2012).

3. B. Ahmad, S.K. Ntouyas, Fractional differential inclusions with fractional separated boundary conditions. Fract. Calc. Appl. Anal. 15, No 3 (2012), 362–382; 10.2478/s13540-012-0027-y; https://www.degruyter.com/view/j/fca.2012.15.issue-3/issue-files/fca.2012.15.issue-3.xml.

4. H. Ahmed, Controllability for Sobolev type fractional integrodifferential systems in a Banach space. Adv. Difference Equ. 2012 (2012), # 167, 10 pp.

5. K. Balachandran, V. Govindaraj, L. Rodrguez-Germa, J.J. Trujillo, Controllability results for nonlinear fractional-order dynamical systems. J. Optim. Theory Appl. 156 (2013), 33–44.

Cited by 41 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Controllability of nonlinear fractional integrodifferential systems involving multiple delays in control;An International Journal of Optimization and Control: Theories & Applications (IJOCTA);2024-01-07

2. Approximate controllability of higher order Riemann–Liouville fractional systems via cosine family;Mathematical Methods in the Applied Sciences;2023-10-31

3. Controllability of Hilfer fractional Langevin evolution equations;Frontiers in Applied Mathematics and Statistics;2023-05-18

4. Controllability results for Sobolev type $ \psi - $Hilfer fractional backward perturbed integro-differential equations in Hilbert space;Evolution Equations and Control Theory;2023

5. On the stability of a strongly stabilizing control for degenerate systems in Hilbert spaces;Demonstratio Mathematica;2023-01-01