Constructive Fractional Analysis with Applications

This book provides a comprehensive overview of constructive and computational fractional analysis, covering ordinary and fractional approximations by positive sublinear operators, high order approximation by multivariate generalized Picard, Gauss-Weierstrass, Poisson-Cauchy, and trigonometric singular integrals, and applications to various types of inequalities, including Opial, Hardy, Hilbert-Pachpatte, and spherical shell inequalities. It is suitable for researchers, graduate students, and seminars in pure and applied mathematics, as well as science and engineering libraries.

Format: Paperback / softback
Length: 522 pages
Publication date: 02 April 2022
Publisher: Springer Nature Switzerland AG

This comprehensive book delves into the realm of constructive approximation theory, encompassing both ordinary and fractional approximations through positive sublinear operators, as well as high-order approximation through multivariate generalized Picard, Gauss-Weierstrass, Poisson-Cauchy, and trigonometric singular integrals. With its increasing significance in mathematics due to its vast real-world applications, Constructive and Computational Fractional Analysis has emerged as a focal point in the field. Authored by the esteemed author, this book presents original research at a broad level, aiming to encompass a wide range of cases across various domains.

The author employs generalized fractional differentiation techniques of Riemann-Liouville, Caputo, and Canavati types, as well as fractional variable order, to address a diverse array of inequalities, including those of Opial, Hardy, Hilbert-Pachpatte, and on the spherical shell. This exploration continues with E. R. Love's left- and right-side fractional integral inequalities, which are further developed in all possible directions. The book culminates in the proof of right-side multivariate fractional Taylor formulae for specific purposes.

The results obtained in this book are anticipated to have widespread applications in both pure and applied mathematics. As such, it serves as an invaluable resource for researchers, graduate students, and seminar participants in these disciplines, as well as being an essential addition to all science and engineering libraries.

Weight: 819g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030714833
Edition number: 1st ed. 2021