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Acknowledgement and thanks
1 Basic definitions and propositions
2 Basics of fractional calculus and fractional order differential
3 Essential of the transmutations
4 Weighted generalized functions generated by quadratic form
5 Buschman-Erdelyi integral and transmutation operators
6 Integral transforms compositions method for transmutations
7 Differential equations with Bessel operator
8 Applications of transmutations to the different problems
9 Fractional powers of Bessel operators
10 B-potentials theory
11 Fractional differential equations with singular coefficients
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"
Researchers, students working in the area of partial differential equations. Advanced undergraduate students, postgraduate students, researchers interested in new methods in differential equations and mathematical physics
- No. of pages:
- © Academic Press 2020
- 1st August 2020
- Academic Press
- Paperback ISBN:
Elina Shishkina works in University of Voronezh State University, Voronezh, Russia and Information Technology and Management in Rzeszow, Rzeszow, Poland. Her research focuses on singular differential equations, fractional powers of differential and integral operators, embedding theorems and integral transforms. She earned a specialist in mathematics in 2004 at Voronezh State University, Voronezh, Russia and PhD in mathematics in 2006 from the same university. She started scientific work in 2004 under the guidance of Professor L. N. Lyakhov. In 2019 The International Society for Analysis, its Applications and Computation (ISAAC) presents to E. Shishkina the life membership for achievements in Integral Transforms, Operator Theory, PDE. She is an author of more than 50 articles and 2 monographs.
Voronezh State University (VSU), Russia
Sergei Sitnik is a Professor at the Chair of Applied Mathematics and Computer Modeling, Institute of Engineering and Digital Technologies, at Belgorod State National Research University (“BSU”), Belgorod, Russia. Не started scientific work on transmutations and PDE theory in 1980s in Voronezh University under the guidance of Professors I. A. Kipriyanov and V. V. Katrakhov. 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 modeling. S. M. Sitnik is an author of approximately 350 scientific papers and 2 monographs.
Belgorod State National Research University (“BelGU”), Russia
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