Analytical Inequalities in Fractional Calculus : Hardy, Opial and Related Inequalities

ISBN-13: 9786200482426 / Angielski

Sajid Iqbal; Josip Pecaric; Zivorad Tomovski

Opis

The main motivation for writing this book is to present some aspects of generalisations, refinements, and variants of famous Hardy, Opial and related inequalities involving kernels. Namely, integral operators with general non-negative kernel on measure spaces with positive $sigma$-finite measure are considered and some new weighted Hardy type inequalities for convex functions and refinements of weighted Hardy type inequalities for super-quadratic functions are obtained. Particularly we have consider Riemann Liouville fractional integral, Hilfer fractional derivative, fractional integral operator which contains generalized Mittag-Leffler functions in the kernel, generalized fractional integral operator with Gauss hypergeometric function, Widder derivative and linear differential operator. Moreover, some refinements of weighted Hardy and Opial type inequalities for convex functions and new refinements of discrete Hardy type inequalities are presented.

O autorze

Iqbal, Sajid
S. Iqbal is serving as an Assistant Professor of Mathematics at University of Management and Technology Lahore, Sialkot Campus. J. Pecaric is a Croatian professor of mathematics and he published over 1800 articles. Z. Tomovski is a Full Professor and he has published over 100 research articles in international journals and one Springer monograph.