Results on approximate controllability for non-densely defined Hilfer fractional differential system with infinite delay

• Published in: Chaos, solitons and fractals Vol. 139; p. 110019
• Main Authors: Vijayakumar, V., Udhayakumar, R.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2020
• Subjects: Approximate controllability; Hilfer fractional differential inclusions; Integrated semigroup; Nonlocal conditions; 34K30; Nonlocal conditions; Approximate controllability; 93B05; 35R10; Integrated semigroup; Hilfer fractional differential inclusions
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2020.110019

•This manuscript is mainly focusing on approximate controllability for non-densely defined Hilfer fractional differential system with infinite delay.•We study our primary outcomes by employing fractional calculus and Bohnenblust-Karlin’s fixed point theorem.•Then, we continue our study to prove the approximate controllability of the Hilfer fractional system with nonlocal conditions.•Lastly, we give two applications to support the validity of the study. This manuscript is mainly focusing on approximate controllability for non-densely defined Hilfer fractional differential system with infinite delay. We study our primary outcomes by employing fractional calculus and Bohnenblust-Karlin’s fixed point theorem. Then, we continue our study to prove the approximate controllability of the Hilfer fractional system with nonlocal conditions. Lastly, we give two applications to support the validity of the study.