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商品描述
This book is devoted to a systematic and comprehensive study of existence, stability, boundary value problems, oscillatory behavior, and linear systems associated with generalized quantum impulsive differential equations. Generalized β-Impulsive Equations aims to provide both a rigorous theoretical foundation and practical analytical tools for researchers, graduate students, and specialists working in nonlinear analysis, dynamic equations, and applied mathematics.
In recent decades, the rapid development of quantum calculus--calculus without limits--together with the theory of impulsive differential equations has opened new and fertile directions for research. The synthesis of these two domains has led to the emergence of generalized quantum impulsive differential equations, a field that captures both discrete-continuous hybrid behavior and sudden state changes within a non-classical calculus setting.
This book aims to provide both a rigorous theoretical foundation and practical analytical tools for researchers, graduate students, and specialists working in nonlinear analysis, dynamic equations, and applied mathematics.
商品描述(中文翻譯)
本書致力於系統性且全面地探討與廣義量子脈衝微分方程相關的存在性、穩定性、邊界值問題、振盪行為，以及線性系統。Generalized β-Impulsive Equations 旨在為從事非線性分析、動態方程與應用數學研究的研究人員、研究生及專業人士，提供嚴謹的理論基礎與實用的分析工具。
近幾十年來，量子微積分（quantum calculus）——一種不使用極限的微積分——迅速發展，並與脈衝微分方程理論相互結合，開創了嶄新且充滿潛力的研究方向。這兩個領域的融合促成了廣義量子脈衝微分方程的興起。此領域在非經典微積分的架構下，同時捕捉離散—連續混合行為與狀態的突發變化。
本書旨在為從事非線性分析、動態方程與應用數學研究的研究人員、研究生及專業人士，提供嚴謹的理論基礎與實用的分析工具。
作者簡介
Svetlin G. Georgiev has worked in various areas of mathematics. He currently focuses on harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and Quaternion analysis, integral equations, dynamic calculus on time scales. He has authored several books for CRC press, including: Boundary Value Problems on Time Scales Volume I, (2021); Boundary Value Problems on Time Scales Volume II, (2021); Multiple Fixed Point Theorems and Applications in the Theory of ODEs, FDEs and PDEs, (2022); Multiplicative Differential Calculus, (2022); Multiplicative Analytic Geometry, (2022); Multiplicative Differential Equations- Volume I, (2023); Multiplicative Differential Equations- Volume II, (2023); Multiplicative Partial Differential Equations, (2023); General Quantum Numerical Analysis, (2024); General Quantum Variational Calculus, (2024); Fuzzy Impulsive Dynamic Equations on Time Scales, (2025).
Khaled Zennir is a professor at Qassim University, Saudi Arabia. His research interests lie in nonlinear partial differential equations, stochastic dynamic equations, fractional derivatives. He has published more than twelve books with CRC Press, including: Boundary Value Problems on Time Scales Volume I, (2021); Boundary Value Problems on Time Scales Volume II, (2021); Multiple Fixed Point Theorems and Applications in the Theory of ODEs, FDEs and PDEs, (2022); Multiplicative Differential Calculus, (2022); Multiplicative Analytic Geometry, (2022); Multiplicative Differential Equations- Volume I, (2023); Multiplicative Differential Equations- Volume II, (2023); Multiplicative Partial Differential Equations, (2023); General Quantum Numerical Analysis, (2024); General Quantum Variational Calculus, (2024); Fuzzy Impulsive Dynamic Equations on Time Scales, (2025).
作者簡介(中文翻譯)
Svetlin G. Georgiev 曾在數學的各個領域從事研究與工作。目前，他專注於調和分析、泛函分析、偏微分方程、常微分方程、Clifford 與 Quaternion 分析、積分方程，以及時間尺度上的動態微積分。他為 CRC Press 撰寫了多本著作，包括：Boundary Value Problems on Time Scales Volume I（2021）；Boundary Value Problems on Time Scales Volume II（2021）；Multiple Fixed Point Theorems and Applications in the Theory of ODEs, FDEs and PDEs（2022）；Multiplicative Differential Calculus（2022）；Multiplicative Analytic Geometry（2022）；Multiplicative Differential Equations—Volume I（2023）；Multiplicative Differential Equations—Volume II（2023）；Multiplicative Partial Differential Equations（2023）；General Quantum Numerical Analysis（2024）；General Quantum Variational Calculus（2024）；Fuzzy Impulsive Dynamic Equations on Time Scales（2025）。
Khaled Zennir 是沙烏地阿拉伯 Qassim University 的教授。他的研究興趣包括非線性偏微分方程、隨機動態方程，以及分數階導數。他已在 CRC Press 出版超過十二本著作，包括：Boundary Value Problems on Time Scales Volume I（2021）；Boundary Value Problems on Time Scales Volume II（2021）；Multiple Fixed Point Theorems and Applications in the Theory of ODEs, FDEs and PDEs（2022）；Multiplicative Differential Calculus（2022）；Multiplicative Analytic Geometry（2022）；Multiplicative Differential Equations—Volume I（2023）；Multiplicative Differential Equations—Volume II（2023）；Multiplicative Partial Differential Equations（2023）；General Quantum Numerical Analysis（2024）；General Quantum Variational Calculus（2024）；Fuzzy Impulsive Dynamic Equations on Time Scales（2025）。
