Generalized fractional calculus : new advancements and applications / George A. Anastassiou.
Anastassiou, George A., 1952- author.
2021
QA314 .A56 2020eb
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Title
Generalized fractional calculus : new advancements and applications / George A. Anastassiou.
Author
Anastassiou, George A., 1952- author.
ISBN
9783030569624 (electronic bk.)
3030569624 (electronic bk.)
3030569616
9783030569617
DOI
https://doi.org/10.1007/978-3-030-56962-4
Published
Cham : Springer, [2021]
Copyright
©2021
Language
English
Description
1 online resource (xv, 498 pages)
Item Number
10.1007/978-3-030-56962-4 doi
Call Number
QA314 .A56 2020eb
Dewey Decimal Classification
515/.352
Summary
This book deals with the quantitative fractional Korovkin type approximation of stochastic processes. Computational and fractional analysis play more and more a central role in nowadays either by themselves or because they cover a great variety of applications in the real world. The author applies generalized fractional differentiation techniques of Caputo, Canavati and Conformable types to a great variety of integral inequalities, e.g. of Ostrowski and Opial types, etc. Some of these are extended to Banach space valued functions. These inequalities have also great impact on numerical analysis, stochastics and fractional differential equations. The author continues with generalized fractional approximations by positive sublinear operators which derive from the presented Korovkin type inequalities, and the author include also abstract cases. The author present also multivariate complex Korovkin quantitative approximation theory. It follows M-fractional integral inequalities of Ostrowski and Polya types. The authors results are weighted so they provide a great variety of cases and applications. The author lays there the foundations of stochastic fractional calculus. The author considers both Caputo and Conformable fractional directions, and the author derives regular and trigonometric results. Our positive linear operators can be expectation operator commutative or not. This book results are expected to find applications in many areas of pure and applied mathematics and stochastics. 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.
Digital File Characteristics
PDF
text file
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed February 4, 2021).
Series
Studies in systems, decision and control ; v. 305.
Available in Other Form
Print version: 9783030569617
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9 Generalized g-Fractional Vector Representation Formula And Bochner Integral Type Inequalities for Banach Space Valued Functions
9.1 Background
9.2 Main Results
References
10 Iterated g-Fractional Vector Bochner Integral Representation Formulae and Inequalities for Banach Space Valued Functions
10.1 Background
10.2 Main Results
References
11 Vectorial Generalized g-Fractional Direct and Iterated Quantitative Approximation by Linear Operators
11.1 Motivation
11.2 Background
11.3 Main Results
References

12 Quantitative Multivariate Complex Korovkin Approximation Theory
12.1 Introduction
12.2 Background
12.3 Main Results
12.4 Applications
References
13 M-Fractional Integral Type Inequalities
13.1 Introduction
13.2 Background
13.3 Main Results
References
14 Principles of Stochastic Caputo Fractional Calculus with Fractional Approximation of Stochastic Processes
14.1 Introduction
14.2 Foundation of Stochastic Fractional Calculus
14.3 Background
14.4 Main Results
14.5 Application
14.6 Stochastic Korovkin Results
References

15 Trigonometric Caputo Fractional Approximation of Stochastic Processes
15.1 Introduction
15.2 Foundation of Stochastic Fractional Calculus (ch1515.10)
15.3 Background (See Also ch1515.10)
15.4 Main Results
15.5 Application
15.6 Trigonometric Stochastic Korovkin Results
References
16 Conformable Fractional Quantitative Approximation of Stochastic Processes
16.1 Introduction
16.2 Background-I
16.3 Background-II
16.4 Main Results
16.5 Application
16.6 Stochastic Korovkin Results
References

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