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Constructive fractional analysis with applications [electronic resource] / George A. Anastassiou.

Anastassiou, George A., 1952-
2021
QA314
Available Online
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Title
Constructive fractional analysis with applications [electronic resource] / George A. Anastassiou.
Author
Anastassiou, George A., 1952-
ISBN
9783030714819 (electronic bk.)
3030714810 (electronic bk.)
9783030714802
3030714802
DOI
https://doi.org/10.1007/978-3-030-71481-9
Published
Cham : Springer, 2021.
Language
English
Description
1 online resource (xv, 522 pages).
Item Number
10.1007/978-3-030-71481-9 doi
Call Number
QA314
Dewey Decimal Classification
515/.83
Summary
This book includes constructive approximation theory; it presents ordinary and fractional approximations by positive sublinear operators, and high order approximation by multivariate generalized Picard, Gauss Weierstrass, Poisson-Cauchy and trigonometric singular integrals. Constructive and Computational Fractional Analysis recently is more and more in the center of mathematics because of their great applications in the real world. In this book, all presented is original work by the author given at a very general level to cover a maximum number of cases in various applications. The author applies generalized fractional differentiation techniques of Riemann-Liouville, Caputo and Canavati types and of fractional variable order to various kinds of inequalities such as of Opial, Hardy, Hilbert-Pachpatte and on the spherical shell. He continues with E.R. Love left- and right-side fractional integral inequalities. They follow fractional Landau inequalities, of left and right sides, univariate and multivariate, including ones for Semigroups. These are developed to all possible directions, and right-side multivariate fractional Taylor formulae are proven for the purpose. It continues with several Gronwall fractional inequalities of variable order. This book results are expected to find applications in many areas of pure and applied mathematics. As such this book is suitable for researchers, graduate students and seminars of the above disciplines, also to be in all science and engineering libraries.
Bibliography, etc. Note
Includes bibliographical references.
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Access limited to authorized users.
Source of Description
Description based on print version record.
Series
Studies in systems, decision and control ; v. 362.
Available in Other Form
Constructive Fractional Analysis with Applications.
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Variable order general fractional integral inequalities
Variable order fractional integral inequalities for spherical shell
Left fractional integral inequalities of E.R. Love type
Right side fractional integral inequalities of E.R. Love type
General fractional Landau inequalities
Abstract fractional Landau inequalities
Fractional Landau inequalities of Riemann-Liouville type
Generalized Canavati fractional Landau inequalities
Sequential left abstract fractional Landau inequalities
Iterated left abstract generalized fractional Landau inequalities
Sequential general right side fractional Landau inequalities
Iterated generalized right side fractional Landau inequalities
High order generalized Landau inequalities
Multidimensional Caputo left side fractional Landau inequalities
Multidimensional left Canavati fractional Landau inequalities
Multidimensional right Caputo fractional Taylor formula and Landau inequalities
Multidimensional generalized right fractional Taylor formula and Landau inequalities
Landau's inequality for semigroups
Fractional variable order Gronwall inequality
A study of Gronwall inequalities of fractional variable order
General ordinary and fractional approximation with positive sublinear operators
Complete approximations with multivariate generalized Picard singular integrals
High order approximation with multivariate generalized Gauss-Weierstrass singular integrals
Complete approximations with multivariate generalized Poisson-Cauchy type singular integral operators
High order approximation with multivariate generalized trigonometric type singular integral operators
Concluding remarks.

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