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Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics

Elina Shishkina (Voronezh State University (VSU), Russia) Sergei Sitnik (Belgorod State National Research University (“BelGU”), Russia)

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English
Academic Press Inc
24 July 2020
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.

By:   , ,
Imprint:   Academic Press Inc
Country of Publication:   United States
Dimensions:   Height: 229mm,  Width: 151mm, 
Weight:   930g
ISBN:   9780128197813
ISBN 10:   0128197811
Series:   Mathematics in Science & Engineering
Pages:   592
Publication Date:  
Audience:   Professional and scholarly ,  Undergraduate
Format:   Paperback
Publisher's Status:   Active
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

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. 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. ?? 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.

Reviews for Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics

"""Publisher’s description: 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."" --zbMATH Open"


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