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

2020-07-24 Mathematics
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Release : 2020-07-24
Genre : Mathematics
Kind : eBook
Book Rating : 079/5 ( reviews)

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Book Synopsis Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics by : Elina Shishkina

Download or read book Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics written by Elina Shishkina. This book was released on 2020-07-24. Available in PDF, EPUB and Kindle. Book excerpt: 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"

Transmutation Operators and Applications

2020-04-11 Mathematics
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Release : 2020-04-11
Genre : Mathematics
Kind : eBook
Book Rating : 14X/5 ( reviews)

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Book Synopsis Transmutation Operators and Applications by : Vladislav V. Kravchenko

Download or read book Transmutation Operators and Applications written by Vladislav V. Kravchenko. This book was released on 2020-04-11. Available in PDF, EPUB and Kindle. Book excerpt: Transmutation operators in differential equations and spectral theory can be used to reveal the relations between different problems, and often make it possible to transform difficult problems into easier ones. Accordingly, they represent an important mathematical tool in the theory of inverse and scattering problems, of ordinary and partial differential equations, integral transforms and equations, special functions, harmonic analysis, potential theory, and generalized analytic functions. This volume explores recent advances in the construction and applications of transmutation operators, while also sharing some interesting historical notes on the subject.

General Fractional Derivatives

2019-05-10 Mathematics
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Release : 2019-05-10
Genre : Mathematics
Kind : eBook
Book Rating : 527/5 ( reviews)

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Book Synopsis General Fractional Derivatives by : Xiao-Jun Yang

Download or read book General Fractional Derivatives written by Xiao-Jun Yang. This book was released on 2019-05-10. Available in PDF, EPUB and Kindle. Book excerpt: General Fractional Derivatives: Theory, Methods and Applications provides knowledge of the special functions with respect to another function, and the integro-differential operators where the integrals are of the convolution type and exist the singular, weakly singular and nonsingular kernels, which exhibit the fractional derivatives, fractional integrals, general fractional derivatives, and general fractional integrals of the constant and variable order without and with respect to another function due to the appearance of the power-law and complex herbivores to figure out the modern developments in theoretical and applied science. Features: Give some new results for fractional calculus of constant and variable orders. Discuss some new definitions for fractional calculus with respect to another function. Provide definitions for general fractional calculus of constant and variable orders. Report new results of general fractional calculus with respect to another function. Propose news special functions with respect to another function and their applications. Present new models for the anomalous relaxation and rheological behaviors. This book serves as a reference book and textbook for scientists and engineers in the fields of mathematics, physics, chemistry and engineering, senior undergraduate and graduate students. Dr. Xiao-Jun Yang is a full professor of Applied Mathematics and Mechanics, at China University of Mining and Technology, China. He is currently an editor of several scientific journals, such as Fractals, Applied Numerical Mathematics, Mathematical Modelling and Analysis, International Journal of Numerical Methods for Heat & Fluid Flow, and Thermal Science.

Fractional Differential Equations

2023-11-20 Technology & Engineering
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Release : 2023-11-20
Genre : Technology & Engineering
Kind : eBook
Book Rating : 384/5 ( reviews)

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Book Synopsis Fractional Differential Equations by : Mouffak Benchohra

Download or read book Fractional Differential Equations written by Mouffak Benchohra. This book was released on 2023-11-20. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the existence and uniqueness results for various classes of problems with periodic conditions. All of the problems in this book deal with fractional differential equations and some fractional derivatives such as the Riemann-Liouville, Caputo and Hilfer fractional derivatives. Classical fixed point theorems as well as the coincidence degree theory of Mawhin are employed as tools.

Fractional Differential Equations And Inclusions: Classical And Advanced Topics

2023-02-02 Mathematics
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Release : 2023-02-02
Genre : Mathematics
Kind : eBook
Book Rating : 27X/5 ( reviews)

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Book Synopsis Fractional Differential Equations And Inclusions: Classical And Advanced Topics by : Said Abbas

Download or read book Fractional Differential Equations And Inclusions: Classical And Advanced Topics written by Said Abbas. This book was released on 2023-02-02. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the existence and stability (Ulam-Hyers-Rassias stability and asymptotic stability) of solutions for various classes of functional differential equations or inclusions involving the Hadamard or Hilfer fractional derivative. Some equations present delay which may be finite, infinite, or state-dependent. Others are subject to impulsive effect which may be fixed or non-instantaneous.Readers will find the book self-contained and unified in presentation. It provides the necessary background material required to go further into the subject and explores the rich research literature in detail. Each chapter concludes with a section devoted to notes and bibliographical remarks and all abstract results are illustrated by examples. The tools used include many classical and modern nonlinear analysis methods such as fixed-point theorems, as well as some notions of Ulam stability, attractivity and the measure of non-compactness as well as the measure of weak noncompactness. It is useful for researchers and graduate students for research, seminars, and advanced graduate courses, in pure and applied mathematics, physics, mechanics, engineering, biology, and all other applied sciences.

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