A new approach on approximate controllability of Sobolev-type Hilfer fractional differential equations

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DOI:

https://doi.org/10.11121/ijocta.2023.1256

Abstract

The approximate controllability of Sobolev-type Hilfer fractional control differential systems is the main emphasis of this paper. We use fractional calculus, Gronwall's inequality, semigroup theory, and the Cauchy sequence to examine the main results for the proposed system. The application of well-known fixed point theorem methodologies is avoided in this paper. Finally, a fractional heat equation is discussed as an example.

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Author Biographies

Ritika Pandey, Department of Electronics Engineering, Rajkiya Engineering College, Kannauj-209732, Uttar Pradesh, India

currently an undergraduate student of electronics engineering. Her interests include control systems and signal processing.

 

Chandan Shukla, Department of Electronics Engineering, Rajkiya Engineering College, Kannauj-209732, Uttar Pradesh, India

currently an undergraduate student of electronics engineering. His interests include control systems and signal processing.

 

Anurag Shukla, Department of Applied Sciences, Rajkiya Engineering College, Kannauj-209732, Uttar Pradesh, India

received M.Sc, and Ph.D. degrees in Mathematics from IIT Roorkee, Uttarakhand, India in 2011, and 2016 respectively. He is an Assistant Professor with the Department of Applied Sciences and Humanities, Rajkiya Engineering College, Kannauj, Uttar Pradesh, India. His current research interests include Fractional Differential Systems, Stochastic Differential Systems, Impulsive Differential Systems, and Mathematical Control theory. To his credit, he has published more than 70 papers in reputed scientific journals.

 

Ashwini Upadhyay, Department of Electronics Engineering, Rajkiya Engineering College, Kannauj-209732, Uttar Pradesh, India

received an M.Tech degree in Electronics Engineering from IIT Kanpur, Uttar Pradesh, India in 2013. Currently, he is an Assistant Professor at the Department of Electronics Engineering, Rajkiya Engineering College, Kannauj, Uttar Pradesh, India. His current research interests include medical image segmentation using deep learning, and mathematical control theory.

 

Arun Kumar Singh, Department of Electronics Engineering, Rajkiya Engineering College, Kannauj-209732, Uttar Pradesh, India

obtained his B.E in Electronics and Instrumentation Engineering from BIET Jhansi in year 1997, M.Tech. in Digital Electronics and Systems, and Ph.D. in the area of distributed systems (Adhoc networks) from Uttar Pradesh Technical University, Lucknow. Presently he is Dean (Academics/PGSR), CoE along with Head of the Electronics Engineering Department at Rajkiya Engineering College, Kannauj, U.P, and has more than 24 years of experience. Dr. Singh is a Fellow member of IE (I), IETE, a Senior member of IEEE, and life member of ISTE. He wrote several books on digital electronics and microcontrollers and got CMI Level 5 Award in Management and Leadership. He contributed research papers in several national and international conferences/journals and also delivered many lectures/keynote address; organised several FDP and workshop/training programs for students and teachers. As a Technologist/Engineer, his interests are: application of technology driven education paradigm, wireless communication, distributed systems, control systems, formal methods, and system modelling.

 

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Published

2023-01-31
CITATION
DOI: 10.11121/ijocta.2023.1256
Published: 2023-01-31

How to Cite

Pandey, R., Shukla, C., Shukla, A., Upadhyay, A., & Singh, A. K. (2023). A new approach on approximate controllability of Sobolev-type Hilfer fractional differential equations. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 13(1), 130–138. https://doi.org/10.11121/ijocta.2023.1256

Issue

Vol. 13 No. 1 (2023): IJOCTA

Section

Research Articles

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Copyright (c) 2023 Ritika Pandey, Chandan Shukla, Anurag Shukla, Ashwini Upadhyay, Arun Kumar Singh

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