Generalized Quantum Calculus with Applications

Auteur
Prof. Svetlin G. Georgiev is a mathematician with a broad range of interests who serves as Professor of Mathematics at Sorbonne University in Paris, France. He has also taught as a Professor of Mathematics and Informatics at Sofia University, St. Kliment Ohridski, Sofia, Bulgaria. Currently, he focuses on ordinary and partial differential equations, harmonic analysis, integral equations, Clifford and quaternion analysis, time scales calculus, and differential and dynamic geometry. Dr. Sanket Tikare is an Assistant Professor in the Department of Mathematics at Ramniranjan Jhunjhunwala College, Mumbai, India. He did his M.Sc. and Ph.D. in Mathematics, both from Shivaji University, Kolhapur, Maharashtra, India. He specializes in Applied Analysis, and his research areas of interest includes differential equations, difference equations, dynamic equations on time scales, impulsive systems, and equations with delays. He has published several research papers (SCOPUS/SCIE) related to the above areas and has collaborated with several eminent researchers from various institutes. He is a life member of the India Mathematical Society and a life member of the International Society of Difference Equations.

Texte du rabat
Generalized Quantum Calculus with Applications is devoted to the qualitative theory of general quantum calculus and its applications to general quantum differential equations and inequalities. The book is aimed at upper-level undergraduate students and beginning graduate students in a range of interdisciplinary courses including physical sciences and engineering, from quantum mechanics to differential equations, with pedagogically organized chapters that each concludes with a section of practical problems. Generalized quantum calculus includes a generalization of the q-quantum calculus and the time scale calculus. There are many open problems and difficulties in q-quantum calculus and time-scale calculus, and this book explores how to use the generalized quantum operators to solve difficulties arising in q-quantum calculus and time-scale calculus, including but not limited to generalized quantum integration, generalized quantum chain rules, and generalized quantum Taylor formula. Since generalized quantum calculus includes the q-quantum and time-scale calculus, this book can be utilized by a wide audience of researchers and students. This text is one of few foundational books on generalized quantum calculus and can be used for future discoveries in the area of integral transforms, variational calculus, integral equations, and inequalities in the language of generalized quantum calculus. This book also offers detailed proofs, exercises, and examples to aid instructors, researchers, and users in their studies.

Contenu

1. Generalized Quantum Differentiation
   
   2. Generalized Quantum Integration
   3. ß-Elementary Functions
   4. The ß-Laplace Transform
   5. First Order Linear ß-Differential Equations
   6. Second Order Linear ß-Differential Equations
   7. ß-Differential Systems
   8. Linear ß- Integral Inequalities