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Generalized Fractional Calculus

Part of the Studies in Systems, Decision and Control Book Series (volume 305)

DOI: 10.1007/978-3-030-56962-4

ISBN: 978-3-030-56961-7

Publisher: Springer International Publishing - Springer Journals

Nov 26, 2020

1 - 10 of 22 Chapters

LitStream

Chapter 1Caputo \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi $$\end{document}-Fractional Ostrowski Inequalities

Anastassiou, George A.

Pages: 1 –12

[Very general univariate mixed Caputo \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}...
LitStream

Chapter 2Caputo \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi $$\end{document}-Fractional Ostrowski and Grüss Inequalities Involving Several Functions

Anastassiou, George A.

Pages: 13 –31

[Very general univariate mixed Caputo \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}...
LitStream

Chapter 3Weighted Caputo Fractional Iyengar Type Inequalities

Anastassiou, George A.

Pages: 33 –68

[Here we present weighted fractional Iyengar type inequalities with respect to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
LitStream

Chapter 4Generalized Canavati g-Fractional Iyengar and Ostrowski Inequalities

Anastassiou, George A.

Pages: 69 –89

[We present here generalized Canavati type g-fractional Iyengar and Ostrowski type inequalities. Our inequalities are with respect to all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}...
LitStream

Chapter 5Generalized Canavati g-Fractional Polya Inequalities

Anastassiou, George A.

Pages: 91 –111

[We present here generalized Canavati type g-fractional Polya type inequalities. We cover also the iterated case. Our inequalities are with respect to all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}...
LitStream

Chapter 6Caputo Generalized \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi $$\end{document}-Fractional Integral Type Inequalities

Anastassiou, George A.

Pages: 113 –133

[Very general univariate and multivariate Caputo \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}...
LitStream

Chapter 7Generalized \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi $$\end{document}-Fractional Quantitative Approximation by Sublinear Operators

Anastassiou, George A.

Pages: 135 –155

[Here we consider the approximation of functions by sublinear positive operators with applications to several Max-Product operators under generalized fractional differentiability. Our study is based on our generalized fractional results about positive sublinear operators. We derive Jackson type...
LitStream

Chapter 8Generalized g-Iterated Fractional Quantitative Approximation By Sublinear Operators

Anastassiou, George A.

Pages: 157 –178

[Here we study the approximation of functions by sublinear positive operators with applications to several Max-Product operators under generalized g -iterated fractional differentiability. Our work is based on our generalized g-iterated fractional results about positive sublinear operators. We...
LitStream

Chapter 9Generalized g-Fractional Vector Representation Formula And Bochner Integral Type Inequalities for Banach Space Valued Functions

Anastassiou, George A.

Pages: 179 –199

[Here we give a very general fractional Bochner integral representation formula for Banach space valued functions. We derive generalized left and right fractional Opial type inequalities, fractional Ostrowski type inequalities and fractional Grüss type inequalities. All these inequalities are...
LitStream

Chapter 10Iterated g-Fractional Vector Bochner Integral Representation Formulae and Inequalities for Banach Space Valued Functions

Anastassiou, George A.

Pages: 201 –221

[Here we present very general iterated fractional Bochner integral representation formulae for Banach space valued functions. Based on these we derive generalized and iterated left and right: fractional Poincaré type inequalities, fractional Opial type inequalities and fractional...

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