New approach on controllability of Hilfer fractional derivatives with nondense domain

Kottakkaran Sooppy Nisar; Kasthurisamy Jothimani; Chokkalingam Ravichandran; Dumitru Baleanu; Devendra Kumar; Kottakkaran Sooppy Nisar; Kasthurisamy Jothimani; Chokkalingam Ravichandran; Dumitru Baleanu; Devendra Kumar

doi:10.3934/math.2022561

AIMS Mathematics

2022, Volume 7, Issue 6: 10079-10095. doi: 10.3934/math.2022561

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New approach on controllability of Hilfer fractional derivatives with nondense domain

1.
Department of Mathematics, College of Arts and Sciences, Prince Sattam Bin Abdulaziz University, Wadi Aldawasir-11991, Saudi Arabia
2.
Department of Mathematics, Sri Eshwar College of Engineering, Coimbatore-641 202, India
3.
Department of Mathematics, Kongunadu Arts and Science College, Coimbatore-641 029, India
4.
Department of Mathematics, Cankaya University, Ankara 06790, Turkey
5.
Institute of Space Sciences, 077125 Magurele-Bucharest, Romania
6.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40447, Taiwan
7.
Department of Mathematics, University of Rajasthan, Jaipur-302004, Rajasthan, India

Received: 14 January 2022 Revised: 17 February 2022 Accepted: 02 March 2022 Published: 21 March 2022
MSC : 34A08, 34K30, 37C25, 46B80, 93B05

This work picturizes the results on the controllability of the nondense Hilfer neutral fractional derivative (HNFD). The uniqueness and controllability of HNFD are discussed with Mönch theorem and Banach contraction technique. In addition, a numerical approximation is given to deal with different criteria of our results.
- controllability,
- Hilfer derivative,
- nondense domain,
- fixed point,
- Banach space,
- fractional calculus
Citation: Kottakkaran Sooppy Nisar, Kasthurisamy Jothimani, Chokkalingam Ravichandran, Dumitru Baleanu, Devendra Kumar. New approach on controllability of Hilfer fractional derivatives with nondense domain[J]. AIMS Mathematics, 2022, 7(6): 10079-10095. doi: 10.3934/math.2022561

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Abstract

This work picturizes the results on the controllability of the nondense Hilfer neutral fractional derivative (HNFD). The uniqueness and controllability of HNFD are discussed with Mönch theorem and Banach contraction technique. In addition, a numerical approximation is given to deal with different criteria of our results.

References

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