This book collects chapters on fixed-point theory and fractional calculus and their applications in science and engineering. It discusses state-of-the-art developments in these two areas through original new contributions from scientists across the world. It contains several useful tools and techniques to develop their skills and expertise in fixed-point theory and fractional calculus. New research directions are also indicated in chapters. This book is meant for graduate students and researchers willing to expand their knowledge in these areas. The minimum prerequisite for readers is the graduate-level knowledge of analysis, topology and functional analysis.
Table of Content
Best Proximity Points for Some Multivalued Contractive Mappings.- Best Proximity Point Theorems via Some Generalized Notions.- New Fixed-Figure Results on Metric Spaces.- Some Fixed Point Results for Suzuki F-Contractions Involving Quadratic Terms in Modular b-Metric Spaces.- Some Common Fixed Point Results via -Series for a Family of JS-Contraction-type Mappings.- Solution of Nonlinear First-Order Hybrid Integro-Differential Equations via Fixed Point Theorem.- Application of Darbo’s Fixed Point Theorem for Existence Result of Generalized 2D Functional Integral Equations.- Results on Generalized Tripled Fuzzy
b-Metric Spaces.- A Novel Controlled Picture Fuzzy Metric Space and Some Related Fixed Point Results.- Theoretical Analysis for a Generalized Fractional-Order Boundary Value Problem.- On Well-posed Variational Problems Involving Multidimensional Integral Functionals.- On the Coupled System of Tempered Fractional Differential Equations with Anti-periodic Boundary Conditions.- Application of Measure of Noncompactness on the Infinite System of Hadamard Fractional Iintegral Equations.- Observability, Reachability, Trajectory Reachability and Optimal Reachability of Fractional Dynamical Systems using Riemann–Liouville Fractional Derivative.- Fractional Calculus Approach to Logistic Equation and its Applications.- Hermite–Hadamard Type Inequalities for Coordinated Quasi-Convex Functions via Generalized Fractional Integrals.- Leray–Schauder Theorem for Implicit Fractional Differential Equation and Nonlocal Multi-Point Conditions.- The
q-Deformed Hamiltonian, Lagrangian, Entropy and Fisher Information.
About the author
PRADIP DEBNATH is Assistant Professor of Mathematics at the Department of Applied Science and Humanities, Assam University, Silchar, India. He received his Ph.D. in Mathematics from the National Institute of Technology Silchar, India. His research interests include fixed-point theory, nonlinear analysis, soft computing, and mathematical statistics. He has published over 60 papers in various journals of international repute and is Reviewer for more than 30 renowned international journals including ‘Mathematical Reviews’ (published by the American Mathematical Society). He is the lead Editor of the books ‘Metric Fixed Point Theory – Applications in Science, Engineering and Behavioural Sciences’ (2021, Springer Nature) and ‘Soft Computing Techniques in Engineering, Health, Mathematical and Social Sciences’ (2021, CRC Press). He has successfully guided several Ph.D. students in the areas of fixed-point theory and soft computing. At present, he is working on a major basic science research project on fixed-point theory funded by the UGC, the Government of India. Having been an academic gold medalist during his post-graduation studies, Dr. Debnath has qualified several national-level examinations in mathematics in India.
H.M. SRIVASTAVA is Professor Emeritus at the Department of Mathematics and Statistics, University of Victoria, Canada. He joined the University of Victoria in 1969 as Associate Professor (1969–1974) and then became Full Professor (1974–2006). Professor Srivastava has held numerous visiting positions including (for example) those at West Virginia University in the U.S.A (1967–1969), Universite Laval in Canada (1975), and the University of Glasgow in the U.K. (1975–1976) and indeed also at many other universities and research institutes in different parts of the world. Professor Srivastava has published 21 books (monographs and edited volumes), 30 book chapters, 45 papers in international conference proceedings, and over1, 000 scientific research journal articles on various topics of mathematical analysis and applicable mathematics. He also has edited (and contributed to) many volumes, which are dedicated to the memories of famous mathematical scientists. Citations of his research contributions can be found in many books and monographs, Ph.D. and D.Sc. theses, and scientific journal articles, much too numerous to be recorded here. Currently, he is actively associated (as editor, honorary editor, senior editor, associate editor, or editorial board member) with over 200 international scientific research journals. Professor Srivastava is a Clarivate Analytics (Web of Science) Highly-Cited Researcher. His biographical sketches (many of which are illustrated with his photograph) have appeared in various issues of more than 50 international biographies, directories, and Who’s Who’s. Professor Srivastava is a Clarivate Analytics (Web of Science) Highly-Cited Researcher.
POOM KUMAM is Full Professor at the Department of Mathematics, King Mongkut’s University of Technology Thonburi (KMUTT), Thailand, where he also is Head of the KMUTT Fixed Point Theory and Applications Research Group, since 2007, and also has led the Theoretical and Computational Science Center (Ta CS-Center) in 2014 (now, the Ta CS-Center of Excellence in 2021). He received the B.S., M.Sc., and Ph.D. degrees in mathematics from Burapha University (BUU), Chiang Mai University (CMU), and Naresuan University (NU), Thailand, respectively. In 2008, he received a grant from the Franco-Thai Cooperation for a short-term visit at the Laboratoire de Mathematiques, Universite de Bretagne Occidentale, France. He was also Visiting Professor for a short-term research with Professor Anthony To-Ming Lau at the University of Alberta, Canada. He has successfully advised five master and 44 Ph.D. students. He served on the editorial boards of various international journals and has published more than 800 papers in Scopus and Web of Science databases. He delivered many invited talks on different international conferences every year all around the world. Furthermore, his research interest focuses on fixed-point theory, fractional differential equations, and optimization, related with optimization problems in both pure science and applied science.
He is awarded the TRF-CHE-Scopus Young Researcher Award in 2010, which is awarded by the corporation of three organizations—Thailand Research Fund (TRF), the Commission of Higher Education (CHE), and Elsevier Publisher (Scopus). He received the TWAS Prize for Young Scientist in Thailand, in 2012, which is given by the Academy of Sciences for the Developing World TWAS (UNESCO) together with the National Research Council of Thailand. In 2014, he received the Fellowship Award for Outstanding Contribution to Mathematics from the International Academy of Physical Science, Allahabad, India. In 2015, He has been awarded the Thailand Frontier Author Awardfor his outstanding research. In 2016, he has been awarded Thailand Frontier Researcher Award on Innovation Forum: Discovery, Protection, Commercialization by Intellectual Property and Science and Thomson Reuters. He also has been Highly Cited Researcher in 2015, 2016, and 2017. He received KMUTT-Hall of Fame 2017, in honour of the recipients of Academic Awards, KMUTT Young Researcher Awards, Excellence in Teaching Awards for 2016. In 2019, he received CMMSE Prize for his contributions to the developments of numerical methods for physics, chemistry, engineering, and economics from the CMMSE Conference. He has also been listed and ranked in the 197th place in general mathematics among the top 2% scientists in the world 2021 (published by Stanford University, U.S.A.).
BIPAN HAZARIKA is Professor at the Department of Mathematics, Gauhati University, Guwahati, Assam, India. Earlier, he was Professor at Rajiv Gandhi University, Rono Hills, Doimukh, Arunachal Pradesh, India, from 2005–2018. He received his Ph.D. degree from Gauhati University, Guwahati, India. His main research interests are in sequences spaces, summability theory, applications fixed-point theory, fuzzy analysis, and function spaces of non-absolute integrable functions. He has published more than 150 research papers in several international journals. He is Regular Reviewer of more than 50 different journals published by Springer Nature, Elsevier, Taylor and Fancis, Wiley, IOS Press, World Scientific, American Mathematical Society, and De Gruyter. He has published books on differential equations, differential calculus, and integral calculus. He is Editorial Board Member for more than five international journals and Guest Editor of special issue “Sequence Spaces, Function Spaces and Approximation Theory”, of Journal of Function Spaces.
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