About the Book
Quantum Calculus and Functional Analysis with Applications presents advanced research on quantum calculus, functional analysis, and their interdisciplinary applications. It focuses on solving complex challenges in areas such as quantum transport, carbon nanotubes, approximation theory, optimal control models, and renewable natural resources by providing cutting-edge developments in these specialised fields. Based on original research, it offers new insights into topics such as neutrosophic normed spaces, probabilistic normed spaces, quantum sequence spaces, and q-calculus applications in functional analysis for innovative applications across fields as diverse as energy, environmental science, and bioengineering.
This book:
• Discusses quantum calculus, fractional calculus, functional analysis, quantization of electromagnetic fields, Caputo-Fabrizio fractional differential equations, q-statistical convergence, and quantum matrix operators
• Explores quantum calculus and fractional calculus applied to quantum functional calculus, biofuels, environmental pollution, and optimal control analysis
• Highlights the role of mathematical methods in addressing challenges in biofuel production and renewable natural resources, making it highly relevant for professionals and researchers in these fields
• Covers new research in fixed point theory, including methods for proving the existence of superior fixed points and applications to nonlinear equations
• Includes theoretical foundations and practical applications, providing a balanced approach that makes complex concepts accessible while maintaining a focus on cutting-edge developments
The book is for researchers and scholars of applied mathematics, and readers interested in the advancement of Quantum Calculus and Functional Analysis.
Table of Contents:
1. Elements of Quantum Calculus 2. Generalized q-Euler Matrix with Associated Sequence Spaces, Duals and Geometric Properties 3. a-Baskakov-Kantorovich Operators Based on q-integers 4. Application of Quantum Calculus for Guided Waves and Quantum Transport in the Carbon Nanotubes 5. Unicity of Meromorphic Functions with respect to kth Derivatives and Differential Polynomials of the Difference Operator 6. Results on Difference Operators of Meromorphic and Entire Functions Sharing Rational Function with Finite Weight 7. Compactness and Essential Norm of C b;c Operators on Bloch-type Space 8. Deferred Riesz Mean in Complex Uncertain Sequences 9. On s-Statistical Convergence in Probabilistic Normed Spaces 10. On Lacunary A-statistical Convergence of Fuzzy Sequences of Order g 11. On I2(Sl;m)□□convergence of Double Sequences in Neutrosophic Normed Linear Spaces 12. Dm□□Statistical Convergence of Order a of Generalized Difference Sequences in Intuitionistic Fuzzy Normed Space13. On Ideal Lacunary Statistical Convergence of Double Sequences in Neutrosophic Normed Spaces 14. Congruences for t-Regular Partitions with Distinct Odd Parts 15. Optimal Control Analysis of Sustainable Consumption of Renewable Natural Resources 16. Some Notes on the Unique Solvability Conditions for Matrix Absolute Value Equations 17. A Family of with-Memory Methods for Solving Nonlinear Equations and their Dynamics 18. Identities Involving Product of Hypergeometric Functions and their Aplications via Fractional Derivative Operator19. An Efficient Numerical Technique via Adomian Decomposition for Bratu’s Problem with Initial Data 20. Coupled Fixed Point of Caputo-Fabrizio Fractional Differential Equations 21. Sequential Extended Modular b-Metric and Sequential Extended Fuzzy b-Metric Spaces 22. Some Results on Extended (c;k2)-Centralizers on Banach *-algebras 23. A Mathematical Analysis of Neural Operator Behaviors
Bibliography
Index
About the Author :
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 2017. He received his PhD degree from the Institute of Advanced Study in Science and Technology at Gauhati University, Guwahati, India. His main research interests include the field of sequences spaces, summability theory, applications fixed point theory, fuzzy analysis, and function spaces of nonabsolute integrable functions. He has published over 200 research papers in several international journals. He is a regular reviewer of more than 50 different journals published by various reputed publishers. 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 specialthe issue “Sequence spaces, Function spaces and Approximation Theory”, Journal of Function Spaces. He has edited a total of five books on different topics of mathematics.
Sanket Tikare is an Assistant Professor in the Department of Mathematics at Ramniranjan Jhunjhunwala College, which is an autonomous college affiliated with the University of Mumbai, Mumbai, Maharashtra, India. He completed his M.Sc. and Ph.D. in Mathematics, both from Shivaji University, Kolhapur, Maharashtra, India. He specialized in Applied Analysis. His research areas of interest include differential equations, difference equations, dynamic equations on time scales, impulsive systems, and equations with delays. He has published several research papers on areas related to the above areas in various journals of international repute. He has collaborated with several eminent researchers from various institutes, which include Missouri Science & Technology, Rolla, Missouri, USA, The University of New South Wales, Sydney, Australia, Texas A&M University-Kingsville, Texas, USA, Universidade Estadual Paulista, Ilha Solterira, Sao Paulo, Brazil, Sorbonne University, Paris, France, National Institute of Technology, Arunachal Pradesh, India, Gauhati University, Guwahati, Assam, India, COEP Technological University, Pune, Maharashtra, India, Manipal University, Jaipur, Rajasthan, India. Dr. Tikare authored four monographs: Stieltjes Differential Calculus and Applications, Set Dynamic Equations on Time Scales, Generalized Quantum Calculus with Applications, and Generalized Quantum Inequalities. He has also edited two edited volumes: Dynamic Equations on Time Scales and Applications, (CRC Press) and Summability, Fixed Point Theory, and Generalized Integrals with Applications (CRC Press). He is a life member of the India Mathematical Society, the International Society of Difference Equations, the Society for Special Functions and their Applications, and the Society for Industrial and Applied Mathematics. Dr. Tikare is a reviewer for many international journals. Moreover, he has written several reviews for Mathematical Reviews (AMS) and Zentralblatt Math (Germany).
Mehmet Dik is a Professor of Mathematics and Chair of the Mathematics, Computer Science, and Physics Department at Rockford University since 2013. His current areas of research and interest are summability theory, subsequential Tauberian theory, Tauberian theorems, undergraduate research, and college teaching. He has published more than 25 research papers. He is a member of the American Mathematical Society, the Turkish Mathematical Society, Sigma Xi the Scientific Research Society, the Mathematical Association of America, and the Northern Illinois Association of Teachers of Mathematics. He is an active reviewer of several renowned journals. Some of them are Journal of Mathematical Analysis and Applications, Linear Algebra and Its Applications, Journal of the Australian Mathematical Society, Aequationes Mathematicae, etc. He is also a reviewer of Zentralblatt fur Mathematik. He is also an editorial board member of several reputed journals of mathematics.
Dimplekumar Chalishajar is a Professor (Colonel-Virginia Militia) of Applied Mathematics at Virginia Military Institute (VMI), Lexington, Virginia, USA (since August 2017); Director of study abroad program, 2017−2019; Chair of International Program Committee (IPC) at VMI, August 2017−August 2019; Chair of VMIRL Liaison Committee, IPC, Institutional Review Board (IRB), since August 2017; Associate Professor at VMI, Lexington, VA, USA (2013−2017); Assistant Professor (Major-Virginia Militia) at VMI, Lexington, VA, USA (2011–2013); Postdoctoral fellow at Virginia Tech (2008−2009); Assistant Professor and Head of the Department, S.V.P. Institute of Technology (SVIT), Gujarat University, India (1998-2008), Lecturer, SVIT, Gujarat University, India (1998−2004); Doctor of Philosophy (Ph.D.): Indian Institute of Science (IISc), Bangalore, and University of Baroda, Vadodara, India; Master of Philosophy (M.Phil.): University of Baroda, Vadodara, India (1996); Master of Science (M.S.): University of Baroda, Vadodara, India (1993); Bachelor of Science (B.S.): University of Baroda, Vadodara, India (1991).He has published more than 100 research articles in highly reputed journals.
