# American Institute of Mathematical Sciences

• Previous Article
Solvability in abstract evolution equations with countable time delays in Banach spaces: Global Lipschitz perturbation
• EECT Home
• This Issue
• Next Article
Approximate controllability of nonlocal problem for non-autonomous stochastic evolution equations
doi: 10.3934/eect.2021016

## Controllability of Hilfer fractional integro-differential equations of Sobolev-type with a nonlocal condition in a Banach space

 Department of Mathematics & Scientific Computing, National Institute of Technology, Hamirpur (H.P.)-177005, India

* Corresponding author: Kamal Jeet (kamaljeetp2@gmail.com)

Received  January 2020 Revised  August 2020 Published  April 2021

Fund Project: The second and third author are supported by CSIR, India under Research Project no-25(0268)/17/EMR-II

This paper aims to establish sufficient conditions for the exact controllability of the nonlocal Hilfer fractional integro-differential system of Sobolev-type using the theory of propagation family $\{P(t), \; t\geq0\}$ generated by the operators $A$ and $R$. For proving the main result we do not impose any condition on the relation between the domain of the operators $A$ and $R$. We also do not assume that the operator $R$ has necessarily a bounded inverse. The main tools applied in our analysis are the theory of measure of noncompactness, fractional calculus, and Sadovskii's fixed point theorem. Finally, we provide an example to show the application of our main result.

Citation: Ankit Kumar, Kamal Jeet, Ramesh Kumar Vats. Controllability of Hilfer fractional integro-differential equations of Sobolev-type with a nonlocal condition in a Banach space. Evolution Equations & Control Theory, doi: 10.3934/eect.2021016
##### References:

show all references

##### References:
 [1] V. Vijayakumar, R. Udhayakumar, K. Kavitha. On the approximate controllability of neutral integro-differential inclusions of Sobolev-type with infinite delay. Evolution Equations & Control Theory, 2021, 10 (2) : 271-296. doi: 10.3934/eect.2020066 [2] Ugo Bessi. Another point of view on Kusuoka's measure. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 3241-3271. doi: 10.3934/dcds.2020404 [3] George A. Anastassiou. Iyengar-Hilfer fractional inequalities. Mathematical Foundations of Computing, 2021  doi: 10.3934/mfc.2021004 [4] Kazeem Olalekan Aremu, Chinedu Izuchukwu, Grace Nnenanya Ogwo, Oluwatosin Temitope Mewomo. Multi-step iterative algorithm for minimization and fixed point problems in p-uniformly convex metric spaces. Journal of Industrial & Management Optimization, 2021, 17 (4) : 2161-2180. doi: 10.3934/jimo.2020063 [5] Isabeau Birindelli, Françoise Demengel, Fabiana Leoni. Boundary asymptotics of the ergodic functions associated with fully nonlinear operators through a Liouville type theorem. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 3021-3029. doi: 10.3934/dcds.2020395 [6] Andrea Cianchi, Adele Ferone. Improving sharp Sobolev type inequalities by optimal remainder gradient norms. Communications on Pure & Applied Analysis, 2012, 11 (3) : 1363-1386. doi: 10.3934/cpaa.2012.11.1363 [7] Iman Malmir. Caputo fractional derivative operational matrices of legendre and chebyshev wavelets in fractional delay optimal control. Numerical Algebra, Control & Optimization, 2021  doi: 10.3934/naco.2021013 [8] Changpin Li, Zhiqiang Li. Asymptotic behaviors of solution to partial differential equation with Caputo–Hadamard derivative and fractional Laplacian: Hyperbolic case. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021023 [9] Huy Dinh, Harbir Antil, Yanlai Chen, Elena Cherkaev, Akil Narayan. Model reduction for fractional elliptic problems using Kato's formula. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021004 [10] Siqi Chen, Yong-Kui Chang, Yanyan Wei. Pseudo $S$-asymptotically Bloch type periodic solutions to a damped evolution equation. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021017 [11] Beom-Seok Han, Kyeong-Hun Kim, Daehan Park. A weighted Sobolev space theory for the diffusion-wave equations with time-fractional derivatives on $C^{1}$ domains. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 3415-3445. doi: 10.3934/dcds.2021002 [12] Peng Luo. Comparison theorem for diagonally quadratic BSDEs. Discrete & Continuous Dynamical Systems, 2021, 41 (6) : 2543-2557. doi: 10.3934/dcds.2020374 [13] Yongqiang Fu, Xiaoju Zhang. Global existence and asymptotic behavior of weak solutions for time-space fractional Kirchhoff-type diffusion equations. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021091 [14] Maoding Zhen, Binlin Zhang, Xiumei Han. A new approach to get solutions for Kirchhoff-type fractional Schrödinger systems involving critical exponents. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021115 [15] Michael Schmidt, Emmanuel Trélat. Controllability of couette flows. Communications on Pure & Applied Analysis, 2006, 5 (1) : 201-211. doi: 10.3934/cpaa.2006.5.201 [16] Charlene Kalle, Niels Langeveld, Marta Maggioni, Sara Munday. Matching for a family of infinite measure continued fraction transformations. Discrete & Continuous Dynamical Systems, 2020, 40 (11) : 6309-6330. doi: 10.3934/dcds.2020281 [17] Christos Sourdis. A Liouville theorem for ancient solutions to a semilinear heat equation and its elliptic counterpart. Electronic Research Archive, , () : -. doi: 10.3934/era.2021016 [18] Sara Munday. On the derivative of the $\alpha$-Farey-Minkowski function. Discrete & Continuous Dynamical Systems, 2014, 34 (2) : 709-732. doi: 10.3934/dcds.2014.34.709 [19] Gbeminiyi John Oyewole, Olufemi Adetunji. Solving the facility location and fixed charge solid transportation problem. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1557-1575. doi: 10.3934/jimo.2020034 [20] Ruchika Sehgal, Aparna Mehra. Worst-case analysis of Gini mean difference safety measure. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1613-1637. doi: 10.3934/jimo.2020037