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Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics
1st Edition - July 24, 2020
Authors: Elina Shishkina, Sergei Sitnik
Language: English
Paperback ISBN:9780128197813
9 7 8 - 0 - 1 2 - 8 1 9 7 8 1 - 3
eBook ISBN:9780128204078
9 7 8 - 0 - 1 2 - 8 2 0 4 0 7 - 8
Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics connects difficult problems with similar more simple ones. The book's st…Read more
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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"
IntroductionAcknowledgement and thanks1 Basic definitions and propositions2 Basics of fractional calculus and fractional order differentialequations3 Essential of the transmutations4 Weighted generalized functions generated by quadratic form5 Buschman-Erdelyi integral and transmutation operators6 Integral transforms compositions method for transmutations7 Differential equations with Bessel operator8 Applications of transmutations to the different problems9 Fractional powers of Bessel operators10 B-potentials theory11 Fractional differential equations with singular coefficientsConclusionReferences
No. of pages: 592
Language: English
Edition: 1
Published: July 24, 2020
Imprint: Academic Press
Paperback ISBN: 9780128197813
eBook ISBN: 9780128204078
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Elina Shishkina
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.
Affiliations and expertise
Voronezh State University (VSU), Russia
SS
Sergei Sitnik
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.
Affiliations and expertise
Belgorod State National Research University (“BelGU”), Russia
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