Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics connects difficult problems with similar more simple ones. The book's strategy works for differential and integral equations and systems and for many theoretical and applied problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methods. In addition to being exposed to recent advances, readers learn to use transmutation methods not only as practical tools, but also as vehicles that deliver theoretical insights.
- Presents the universal transmutation method as the most powerful for solving many problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methods
- Combines mathematical rigor with an illuminating exposition full of historical notes and fascinating details
- Enables researchers, lecturers and students to find material under the single "roof"
1. Basic definitions and propositions 2. Essentials of transmutations 3. Basics of fractional calculus and fractional order differential equations 4. Weighted generalized functions generated by indefinite quadratic form 5. Buschman-Erdelyi integral operators and transmutations 6. Integral transforms compositions method (ITCM) for transmutations 7. Differential equations with Bessel operator (without fractional powers operators) 8. Transmutations for 1D Schrodinger equation 9. B-potentials theory 10. Fractional powers of Bessel operators 11. Differential equations (based on fractional powers operators) 12. Fractional differential equations with singular coefficients 13. Applications of Buschman-Erdelyi integral operators 14. Applications of Euler-Poisson-Darboux differential equations 15. Applications of B-potentials theory and fractional differential equations 16. Different applications
Sergei Sitnik was born in 1961, entered Voronezh State University in 1978, Faculty of Applied Mathematics and Mechanics. After 3 more years of post-graduate teaching graduated from this University in 1986. His supervisors were I.A.Kipriyanov and V.V.Katrakhov. ?? belongs to the famous Voronezh Mathematical School settled by Mark Krasnoselskii and Selim Krein, and continued by the school of I.A.Kipriyanov on singular differential equations. He received Ph.D. degree in 1987 and Doctor Science degree in 2016 from Voronezh State University. In 1989-2016 he worked in Voronezh Polytechnic Institute, Vladivostok Soviet&Russian Academy of Science Institute of Automation and Control Processes, Voronezh Institute of the Ministry of Internal Affairs of Russia. Now he holds positions as Professor at the Chair of Differential Equations, Institute of Engineering and Digital Technologies and Deputy Director of "Nanostructured Materials and Nanotechnologies" Science, Education & Innovation Centre, both at Belgorod State National Research University ("BelGU). In his research he combines theoretical and applied problems. His fields of interest are: transmutation operators, integral transforms and special functions, singular and fractional order differential equations, numerical methods and mathematical modelling. S.M.Sitnik is an author of approximately 350 scientific papers and 2 monographs.
Shishkina, Elina Leonidovna
Elina Shishkina is Associated Professor of Applied Mathematics, Informatics and Mechanics Faculty of Voronezh State University (VSU), Russia. She was born in 1980 in Voronezh, Russia. Her work now focuses on singular differential equations and fractional powers of differential and integral operators. Before coming to VSU for a work, Elina taught at Mathematical Department and Quality Control and Machine-Building Technology Department of Voronezh State Technological Academy. Elina earned a specialist in mathematics in 2004 and a doctorate in mathematics in 2006 from the Voronezh State University. She is an author of more than 50 articles and 1 monograph.