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Operators of Fractional Calculus and Their Applications

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ISBN: 9783038973409 / 9783038973416 Year: Pages: 136 DOI: 10.3390/books978-3-03897-341-6 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Mathematics --- Physics (General)
Added to DOAB on : 2019-01-16 12:17:12
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Abstract

During the past four decades or so, various operators of fractional calculus, such as those named after Riemann–Liouville, Weyl, Hadamard, Grunwald–Letnikov, Riesz, Erdelyi–Kober, Liouville–Caputo, and so on, have been found to be remarkably popular and important due mainly to their demonstrated applications in numerous diverse and widespread fields of the mathematical, physical, chemical, engineering, and statistical sciences. Many of these fractional calculus operators provide several potentially useful tools for solving differential, integral, differintegral, and integro-differential equations, together with the fractional-calculus analogues and extensions of each of these equations, and various other problems involving special functions of mathematical physics, as well as their extensions and generalizations in one and more variables. In this Special Issue, we invite and welcome review, expository, and original research articles dealing with the recent advances in the theory of fractional calculus and its multidisciplinary applications.

Inequalities

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ISBN: 9783039280629 / 9783039280636 Year: Pages: 204 DOI: 10.3390/books978-3-03928-063-6 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Mathematics --- Science (General)
Added to DOAB on : 2020-01-30 16:39:46
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Inequalities appear in various fields of natural science and engineering. Classical inequalities are still being improved and/or generalized by many researchers. That is, inequalities have been actively studied by mathematicians. In this book, we selected the papers that were published as the Special Issue ‘’Inequalities’’ in the journal Mathematics (MDPI publisher). They were ordered by similar topics for readers’ convenience and to give new and interesting results in mathematical inequalities, such as the improvements in famous inequalities, the results of Frame theory, the coefficient inequalities of functions, and the kind of convex functions used for Hermite–Hadamard inequalities. The editor believes that the contents of this book will be useful to study the latest results for researchers of this field.

Keywords

analytic functions --- starlike functions --- convex functions --- Fekete-Szegö inequality --- Hilbert C*-module --- g-frame --- g-Bessel sequence --- adjointable operator --- analytic functions --- starlike functions --- convex functions --- Fekete-Szegö inequality --- operator inequality --- positive linear map --- operator Kantorovich inequality --- geometrically convex function --- frame --- weaving frame --- weaving frame operator --- alternate dual frame --- Hilbert space --- quantum estimates --- Hermite-Hadamard type inequalities --- quasi-convex --- Hermite–Hadamard type inequality --- strongly ?-convex functions --- Hölder’s inequality --- Power mean inequality --- Katugampola fractional integrals --- Riemann–Liouville fractional integrals --- Hadamard fractional integrals --- Steffensen’s inequality --- higher order convexity --- Green functions --- Montgomery identity --- Fink’s identity --- Hermite-Hadamard inequality --- interval-valued functions --- (h1, h2)-convex --- majorization inequality --- twice differentiable convex functions --- refined inequality --- Taylor theorem --- Gronwall–Bellman inequality --- proportional fractional derivative --- Riemann–Liouville and Caputo proportional fractional initial value problem --- convex functions --- Fejér’s inequality --- special means --- weaving frame --- weaving K-frame --- K-dual --- pseudo-inverse --- ?-variation --- one-sided singular integral --- commutator --- one-sided weighted Morrey space --- one-sided weighted Campanato space --- power inequalities --- exponential inequalities --- trigonometric inequalities --- weight function --- half-discrete Hardy-Hilbert’s inequality --- parameter --- Euler-Maclaurin summation formula --- reverse inequality

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