Abstract
AbstractIn this article, we study the controllability for impulsive fractional integro-differential evolution equation in a Banach space. The discussions are based on the Mönch fixed point theorem as well as the theory of fractional calculus and the $(\alpha ,\beta )$
(
α
,
β
)
-resolvent operator, we concern with the term $u'(\cdot )$
u
′
(
⋅
)
and finding a control v such that the mild solution satisfies $u(b)=u_{b}$
u
(
b
)
=
u
b
and $u'(b)=u'_{b}$
u
′
(
b
)
=
u
b
′
. Finally, we present an application to support the validity study.
Funder
National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Reference28 articles.
1. Abada, N., Benchohra, M., Hammouche, H.: Existence and controllability results for nondensely defined impulsive semilinear functional differential inclusions. J. Differ. Equ. 246, 3834–3863 (2009)
2. Aimene, D., Baleanu, D., Seba, D.: Controllability of semilinear impulsive Atangana–Baleanu fractional differential equations with delay. Chaos Solitons Fractals 128, 51–57 (2019)
3. Bai, Z., Lü, H.: Positive solutions for boundary value problem of nonlinear fractional differential equation. J. Math. Anal. Appl. 311, 495–505 (2005)
4. Balachandran, K., Park, J.Y.: Controllability of fractional integrodifferential systems in Banach spaces. Nonlinear Anal. Hybrid Syst. 3, 363–367 (2009)
5. Balachandran, K., Sakthivel, R.: Controllability of integrodifferential systems in Banach spaces. Appl. Math. Comput. 118, 63–71 (2001)
Cited by
9 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