Dynamic Equations on Time Scales and Applications

This book presents the theory of dynamic equations on time scales and applications, providing an overview of recent developments in the foundations of the field as well as its applications. It discusses the recent results related to the qualitative properties of solutions like existence and uniqueness, stability, continuous dependence, controllability, oscillations, etc. Presents cutting-edge research trends of dynamic equations and recent advances in contemporary research on the topic of time scales Connects several new areas of dynamic equations on time scales with applications in different fields Includes mathematical explanation from the perspective of existing knowledge of dynamic equations on time scales Offers several new recently developed results, which are useful for the mathematical modeling of various phenomena Useful for several interdisciplinary fields like economics, biology, and population dynamics from the perspective of new trends The text is for postgraduate students, professionals, and academic researchers working in the fields of Applied Mathematics

Table of Contents:
1 Elements of Time Scales Calculus 2 First Order Functional Dynamic Equations 3 Foundations of Linear Control Theory on Time Scales 4 Optimal Control Theory for Dynamic Equations 5 Controllability of Dynamic Equations 6 Delayed Dynamic Equations with Sp-Terms 7 Integro-Dynamic System with Stepanov-like Coefficients 8 Terminal Value Problems for Discrete Fractional Relaxation Equations 9 Diamond-Alpha Hardy–Copson type Dynamic Inequalities-I 10 Diamond-Alpha Hardy–Copson type Dynamic Inequalities-II 11 Fishing Model with Feedback Control on Time Scales 12 Some Geometric Properties of Dual Space on Time Scales 13 Serret–Frenet Frame of a Curve Parametrized by Time Scales: A Brief Survey 14 Applications of Time Scales in Nature: A Brief Survey 15 Applications of Time Scales in Economics: A Brief Survey Index

About the Author :
In the last fifty years, Ravi P. Agarwal has been one of the most famous, influential, and successful figures in the field of Mathematics. In academia, people typically find their place either as good researchers, mentors, editors, or managers. Ravi P. Agarwal has been able to fulfill each of these roles. He is an excellent researcher, a very successful supervisor, the founder of several esteemed scientific journals, and a perfect administrator. Ravi P. Agarwal was born in Moradabad (India) on July 10, 1947. He earned his Master’s degree from Agra University in 1969, ranking 2nd among over 500 in that year. In 1973, he earned his Ph.D. (Mathematics) at the Indian Institute of Technology in Madras, India, which is one of the highest-ranking universities in India. Since then, for the last 50 years, Dr. Agarwal has been actively involved in research and pedagogical activities. He has made significant contributions in various research fields, including Numerical Analysis, Differential and Difference Equations, Inequalities, and Fixed Point Theorems. He is an excellent scholar, a dedicated teacher, and a prolific researcher. He has published 50 research monographs, and more than 1,800 publications (with almost 700 mathematicians all over the world) in prestigious national and international mathematics journals. Dr. Agarwal has previously worked either as a full-time faculty member or as a visiting professor and scientist in universities in several countries, including India, Germany, Italy, Canada, Australia, USA, Singapore, and Japan. He has held several positions including Visiting Professor, Visiting Scientist, and Professor at various universities in different parts of the world. Specifically, from 1980 to 1981, he was awarded the most prestigious Alexander Von Humboldt Foundation Fellowship to work with Prof. Dr. G. Hammerlin at the Ludwig-Maximilians Universitat, Munchen, Germany. From 1981 to 1982, he worked as a Visiting Professor with Prof. Roberto Conti, at the Instituto Matematico, Firenze, Italy. He has been ranked as a Highly Cited Researcher for 14 consecutive years, and has also been recognized as one of the “World’s Most Influential Scientific Minds” in 2014 and 2015 by Thomas Reuters/Clarivate Analytics (world’s most prestigious scientific organization). In 2021, he was listed among world’s top 2% Scientists by Stanford University (https://1drv.ms/x/s!Ag-47qfFs 0OhgFG7xpiw6uqkDeM?e=K0hNpf), his ranking is 6734 out of 186178. In 2022, Dr. Agarwal has been ranked 20th among 100 Top Mathematics Scientists by Research.com (https://research.com/scientists-rankings/mathematics). According to Google Scholar, Dr. Agarwal has been cited more than 70,000 times. On Math-SciNet, his work has been cited more than 17,700 times by 7,400 scientists. Dr. Agarwal is the recipient of several notable honors and awards, including Doctor Honoris Causa (2015 by the University of Constanta, Romania), Professor Honoris Causa (2015 by the University of Cluj, Romania), Honorary Doctorate (2017 by the University of Nis, Serbia), Doctor Honoris Causa (2017 by Plovdiv University, Bulgaria), Doctor Honoris Causa (2017 by Constantin Brancusi, University of Targu-Jiu, Romania), Doctor Honoris Causa (2017 by University of Oradea, Romania, 2017), Doctor Honoris Causa (by 1 December 1918, University of Alba Lulia, Romania), Honorary Doctorate (2019 by Istanbul Gelisim University, Turkey), and Doctor Honoris Causa (2019 by Transilvania University of Brasov, Romania). He was also nominated as a possible candidate for the Banco Bilbao Vizcaya Argentaria (BBVA) Foundation Frontiers of Knowledge Award, an international award scheme recognizing significant contributions in the areas of scientific research and cultural creation. Many BBVA award winners are Nobel laureates, including Stephen Hawkings. Florida Institute of Technology (USA) and King Abdulaziz University have recently offered him a Distinguished University Professorship of Mathematics. Dr. Agarwal has provided significant service to Texas A&M University-Kingsville. Under his leadership during 2011-19, the Department of Mathematics consistently progressed in education and preparation of students, and in new directions of research. His overall impact to the university is considerable. Many scholars from different countries, including China, Turkey, India, and Korea have come to work under his guidance. The majority of these visiting post-doctoral scholars were sent to work under Dr. Agarwal by their employing institutions for at least one year. Dr. Agarwal regularly presents his research at invited talks/colloquiums (over 100 institutions worldwide). He has been invited to give plenary/keynote lectures at international conferences in the USA, Russia, Italy, India, Portugal, Poland, Spain, Vietnam, China, Taiwan, Korea, Malaysia, Thailand, Romania, Saudi Arabia, Germany, Canada, Singapore, Turkey, Ukraine, Greece, and Japan. He has served as Editor/Honorary Editor or Associate Editor in over 40 Journals and has published 20 books as editor. Dr. Agarwal has also organized International Conferences. In summary of these few inadequate paragraphs, Dr. Ravi P. Agarwal is a visionary scientist, educator, mentor, organizer, and administrator who has contributed to the world through his long service, dedication, and tireless efforts. Bipan Hazarika is currently a Professor in the Department of Mathematics at Gauhati University, Guwahati, Assam, India. Before joining Gauhati University he worked as a Professor at Rajiv Gandhi University, Rono Hills, Doimukh, Arunachal Pradesh, India from 2005 to 2018. He received his PhD degree from Gauhati University, Guwahati, India. His main research interests includes the field of sequences spaces, summability theory, applications fixed point theory, fuzzy analysis, function spaces of nonabsolute integrable functions. He has published over 200 research papers in several international journals. He is regular reviewer of more than 50 different journals published from Springer, Elsevier, Taylor and Francis, Wiley, IOS Press, World Scientific, American Mathematical Society, De Gruyter, etc. He has published books on Differential Equations, Differential Calculus and Integral Calculus. He is an editorial board member of more than 5 International Journals and Guest Editor of special the issue “Sequence spaces, Function spaces and Approximation Theory”, Journal of Function Spaces. He has edited five books on different topics of mathematics, out of them two are published by CRC Press and three are published by Springer. Sanket Tikare is an Assistant Professor in the Department of Mathematics, at Ramniranjan Jhunjhunwala College, Mumbai, India, which is an empowered autonomous college affiliated with the University of Mumbai, India. He did his M.Sc. and Ph.D. in Mathematics, both from Shivaji University, Kolhapur, India in the years 2008 and 2012 respectively. He is specialized in Applied Analysis. His research area of interest includes time scale theory, dynamic equations on time scales, differential equations, difference equations, fractional equations. He has published several research papers in international journals. He has collaborated with several eminent researchers from various institutes around the globe. He is member of a life member of the Indian Mathematical Society, a life member of the International Society of Difference Equations. Sanket Tikare is a regular reviewers of many highly-reputed international journals. Moreover, he has written reviews on several articles for Mathematical Reviews (AMS) and Zentralblatt Math (Germany). He has delivered invited talks at 20 international conferences. He has also delivered several contributed talks at various conferences in India and abroad.