Quantum Calculus and Functional Analysis with Applications

Bipan Hazarika, Sanket Tikare, Mehmet Dik, Dimplekumar Chalishajar

• Publisher: Chapman and Hall/CRC
• Year: 2025
• eBook ISBN: 9781040439128
• Topic: Physical Sciences
• Subtopic: Applied Mathematics

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

• Cover Page
• Half-Title Page
• Title Page
• Copyright Page
• Contents
• Preface
• Editor Biography
• Contributors
• 1 Elements of Quantum Calculus
• 2 Generalized q-Euler Matrix with Associated Sequence Spaces, Duals, and Geometric Properties
• 3 α-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 κth 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 Cb,c Operators on Bloch-type Space
• 8 Deferred Riesz Mean in Complex Uncertain Sequences
• 9 On σ-Statistical Convergence in Probabilistic Normed Spaces
• 10 On Lacunary A-statistical Convergence of Fuzzy Sequences of Order γ
• 11 On I2(Sλ,μ)− convergence of Double Sequences in Neutrosophic Normed Linear Spaces
• 12 Δm-Statistical Convergence of Order α of Generalized Difference 00 Sequences in Intuitionistic Fuzzy Normed Space
• 13 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 Operator
• 19 An Efficient Numerical Technique via Adomian Decomposition for Bratu's Problem with Initial Data
• 20 Coupled Fixed Points 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
• A Proofs of Theorems, Lemmas, and Conjectures
• Index