New approach on controllability of Hilfer fractional derivatives with nondense domain-Reference-Cited by-同舟云学术

New approach on controllability of Hilfer fractional derivatives with nondense domain

Published:2022 Issue:6 Volume:7 Page:10079-10095
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Nisar Kottakkaran Sooppy¹,Jothimani Kasthurisamy²,Ravichandran Chokkalingam³,Baleanu Dumitru⁴⁵⁶,Kumar Devendra⁷

Affiliation:

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

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference40 articles.

1. P. Agarwal, D. Baleanu, Y. Q. Chen, S. Momani, J. A. T. Machado, Fractional calculus, Singapore: Springer, 2018. https://doi.org/10.1007/978-981-15-0430-3

2. K. Diethelm, The analysis of fractional differential equations, Berlin: Springer-Verlag, 2004. https://doi.org/10.1007/978-3-642-14574-2

3. X. L. Fu, On solutions of neutral nonlocal evolution equations with non-dense domain, J. Math. Anal. Appl., 299 (2004), 392–410. https://doi.org/10.1016/j.jmaa.2004.02.062

4. X. L. Fu, X. B. Liu, Controllability of non-densely defined neutral functional differential systems in abstract space, Chin. Ann. Math. Ser. B, 28 (2007), 243–252. https://doi.org/10.1007/S11401-005-0028-9

5. K. M. Furati, M. D. Kassim, N. E. Tatar, Existence and uniqueness for a problem involving Hilfer fractional derivative, Comput. Math. Appl., 64 (2012), 1616–1626. https://doi.org/10.1016/j.camwa.2012.01.009

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