This book presents generalized Caputo fractional Ostrowski and Grüss-type inequalities involving several Banach algebra valued functions. Furthermore, the author gives generalized Canavati fractional Ostrowski, Opial, Grüss, and Hilbert-Pachpatte-type inequalities for multiple Banach algebra valued functions. By applying the p-Schatten norms over the von Neumann–Schatten classes, the author produces the analogous refined and interesting inequalities. The author provides many applications. This book’s results are expected to find applications in many areas of pure and applied mathematics, especially in fractional inequalities and fractional differential equations. Other interesting applications are in applied sciences like geophysics, physics, chemistry, economics, and engineering. This book is appropriate for researchers, graduate students, practitioners, and seminars of the above disciplines, also to be in all science and engineering libraries.
Author(s): George A. Anastassiou
Series: Studies in Systems, Decision and Control, 441
Publisher: Springer
Year: 2022
Language: English
Pages: 311
City: Cham
Preface
Contents
1 Generalized Fractional Ostrowski and Grüss Inequalities with Multiple Banach Algebra Valued Functions
1.1 Introduction
1.2 Vectorial Background Fractional Calculus
1.3 Banach Algebras Background
1.4 Main Results
1.5 Applications
References
2 Iterated Generalized Fractional Ostrowski and Grüss Inequalities with Multiple Banach Algebra Valued Functions
2.1 Introduction
2.2 Vectorial Sequential Generalized Fractional Calculus Background
2.3 Banach Algebras Background
2.4 Main Results
2.5 Applications
References
3 Generalized Canavati Fractional Ostrowski, Opial and Grüss Inequalities with Multiple Banach Algebra Valued Functions
3.1 Introduction
3.2 Background on Vectorial Generalized Canavati Fractional Calculus
3.3 Banach Algebras Background
3.4 Main Results
3.5 Applications
3.6 Addendum
References
4 Generalized Canavati Fractional Hilbert–Pachpatte Inequalities for Banach Algebra Valued Functions
4.1 Introduction
4.2 Background on Vectorial Generalized Canavati Fractional Calculus
4.3 Banach Algebras Background
4.4 Main Results
4.5 Applications
References
5 Generalized Ostrowski, Opial and Hilbert-Pachpatte Inequalities for Banach Algebra Valued Functions Involving Integer Vectorial Derivatives
5.1 Introduction
5.2 About Banach Algebras
5.3 Background
5.4 Main Results
5.5 Applications
References
6 Multivariate Ostrowski Inequalities for Several Banach Algebra Valued Functions
6.1 Introduction
6.2 About Banach Algebras
6.3 Vector Analysis Background
6.4 Main Results
References
7 p-Schatten Norm Generalized Fractional Ostrowski and Grüss Inequalities for Multiple Functions
7.1 Introduction
7.2 Vectorial Background Fractional Calculus
7.3 Banach Algebras Background
7.4 p-Schatten Norms Background
7.5 Main Results
7.6 Applications
References
8 p-Schatten Norm Iterated Generalized Fractional Ostrowski and Grüss Inequalities for Multiple Functions
8.1 Introduction
8.2 Vectorial Sequential Generalized Fractional Calculus Background
8.3 Banach Algebras Basic Background
8.4 p-Schatten Norms Background
8.5 Main Results
8.6 Applications
References
9 p-Schatten Norm Generalized Canavati Fractional Ostrowski, Opial and Grüss Inequalities for Multiple Functions
9.1 Introduction
9.2 Background on Vectorial Generalized Canavati Fractional Calculus
9.3 Basic Banach Algebras Background
9.4 p-Schatten Norms Background
9.5 Main Results
9.6 Applications
References
10 γ-Schatten Norm Generalized Canavati Fractional Hilbert–Pachpatte Inequalities with von Neumann–Schatten Class mathcalBγ( H) Valued Functions
10.1 Introduction
10.2 Background on Vectorial Generalized Canavati Fractional Calculus
10.3 Basic Banach Algebras Background
10.4 p-Schatten Norms Background
10.5 Main Results
10.6 Applications
References
11 γ-Schatten Norm Generalized Ostrowski, Opial and Hilbert–Pachpatte Inequalities with von Neumann–Schatten Class mathcalBγ( H) Valued Functions Using Ordinary Vectorial Derivatives
11.1 Introduction
11.2 Background
11.3 About Basic Banach Algebras
11.4 p-Schatten Norms Background
11.5 Main Results
11.6 Applications
References
12 γ-Schatten Norm Multivariate Ostrowski Inequalities for Multiple Neumann–Schatten Class mathcalBγ(H) Valued Functions
12.1 Introduction
12.2 About Banach Algebras
12.3 p-Schatten Norms Background
12.4 Vector Analysis Background
12.5 Main Results
References
13 Conclusion
