This book demonstrates the unifying methods of generalized versions of Hilfer, Prabhakar and Hilfer–Prabhakar fractional calculi, and we establish related unifying fractional integral inequalities of the following types: Iyengar, Landau, Polya, Ostrowski, Hilbert–Pachpatte, Hardy, Opial, Csiszar’s f-Divergence, self-adjoint operator and related to fuzziness. Our results are univariate and multivariate. 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 can be 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, 398
Publisher: Springer
Year: 2021
Language: English
Pages: 419
City: Cham
Preface
Contents
1 Progress on Generalized Hilfer Fractional Calculus and Fractional Integral Inequalities
1.1 Introduction
1.2 Background
1.3 Main Results
1.3.1 New Advancements to Hilfer Fractional Calculus
1.3.2 Basic Integral Inequalities Involving Hilfer Fractional Calculus
References
2 Landau Generalized Hilfer Fractional Inequalities
2.1 Introduction
2.2 Background
2.3 Main Results
References
3 Iyengar-Hilfer Generalized Fractional Inequalities
3.1 Introduction
3.2 Background
3.3 Main Results
3.3.1 Univariate Results
3.3.2 Multivariate Results
3.4 Application
References
4 Generalized Hilfer-Polya, Hilfer-Ostrowski and Hilfer-Hilbert-Pachpatte Fractional Inequalities
4.1 Introduction
4.2 Background
4.3 Main Results
References
5 Generalized Hilfer Fractional Approximation of Csiszar's f-Divergence
5.1 Background-I
5.2 Background-II
5.3 Main Results-I
5.4 Background-III
5.5 Main Results-II
References
6 Generalized Hilfer Fractional Self Adjoint Operator Inequalities
6.1 Background—I
6.2 Background—II
6.3 Main Results
References
7 Essential Forward and Reverse Generalized Hilfer-Hardy Fractional Inequalities
7.1 Background
7.2 Main Results
References
8 Principles of Generalized Prabhakar-Hilfer Fractional Calculus and Applications
8.1 Background
8.2 Main Results
8.3 Appendix
References
9 Advanced and General Hilfer-Prabhakar-Hardy Fractional Inequalities
9.1 Background
9.2 Main Results
References
10 Vectorial Advanced Hilfer-Prabhakar-Hardy Fractional Inequalities
10.1 Background
10.2 Prerequisites
10.3 Main Results
References
11 Vectorial Prabhakar Hardy Advanced Fractional Inequalities Under Convexity
11.1 Background
11.2 Prerequisites
11.3 Main Results
References
12 Advanced Multivariate Prabhakar fractional integrals and inequalities
12.1 Background
12.2 Prerequisites
12.3 Main Results
References
13 Non Singular Kernel Multiparameter Fractional Differentiation
13.1 Background
13.2 Main Results
References
14 Advanced Hilfer Fractional Opial Inequalities
14.1 Background
14.2 Main Results
14.2.1 Results involving one Function
14.2.2 Results Involving Two Functions
14.2.3 Results Involving Several Functions
References
15 Exotic Fractional Integral Inequalities
15.1 Background
15.2 Prerequisites
15.3 Main Results
References
16 Fuzzy Fractional Calculus
16.1 Fuzzy Mathematical Analysis Needed
16.2 Fractional Calculus Background
16.3 Main Results
References
17 Conclusion
