Advances on Fractional Inequalities by George A. Anastassiou PDF

By George A. Anastassiou

ISBN-10: 1461407028

ISBN-13: 9781461407027

Advances on Fractional Inequalities use essentially the Caputo fractional spinoff, because the most crucial in functions, and provides the 1st fractional differentiation inequalities of Opial style which includes the balanced fractional derivatives. The booklet keeps with correct and combined fractional differentiation Ostrowski inequalities within the univariate and multivariate situations. subsequent the best and left, in addition to combined, Landau fractional differentiation inequalities within the univariate and multivariate circumstances are illustrated. during the publication many purposes are given.

Fractional differentiation inequalities are by means of themselves a tremendous and nice mathematical subject for examine. additionally they've got many functions, an important ones are in developing strong point of resolution in fractional differential equations and platforms and in fractional partial differential equations. additionally they supply higher bounds to the recommendations of the above equations.

Fractional Calculus has emerged as very important over the past 40 years as a result of its many functions in just about all technologies. this is often presently obvious in functions in acoustic wave propagation in inhomogeneous porous fabric, diffusive delivery, fluid movement, dynamical procedures in self-similar buildings, dynamics of earthquakes, optics, geology, viscoelastic fabrics, bio-sciences, bioengineering, medication, economics, chance and facts, astrophysics, chemical engineering, physics, splines, tomography, fluid mechanics, electromagnetic waves, nonlinear regulate, sign processing, regulate of energy digital, converters, chaotic dynamics, polymer technological know-how, proteins, polymer physics, electrochemistry, statistical physics, rheology, thermodynamics, neural networks, and so forth. just about all fields of study in technology and engineering use fractional calculus so one can describe results.

This ebook is part of Fractional Calculus, hence it truly is worthy for researchers and graduate scholars for examine, seminars and complex graduate classes, in natural and utilized arithmetic, engineering and all different utilized sciences.

Show description

Read or Download Advances on Fractional Inequalities PDF

Similar calculus books

Read e-book online Boundary elements: an introductory course PDF

Boundary options are brought and instantly utilized in easy - yet priceless - machine codes. those codes facilitate the comprehension of boundary parts. this article additionally discusses simple suggestions, capability difficulties, elastostatics and different subject matters of curiosity to engineers.

Download PDF by Vladimir I. Arnol'd: Huygens and Barrow, Newton and Hooke: pioneers in

В книге написанной на основе лекции для студентов, рассказывается о рождении современной математики и теоретической физики в трудах великих ученых XVII века. Некоторые идеи Ньютона и Гюйгенса опередили свое время на несколько столетий и получили развитие только в последние годы. Об этих идеях, включая несколько новых результатов, также расказано в книге.

Download e-book for iPad: Moduli of Riemann Surfaces, Real Algebraic Curves, and Their by S. M. Natanzon

The gap of all Riemann surfaces (the so-called moduli area) performs a huge function in algebraic geometry and its purposes to quantum box concept. the current booklet is dedicated to the research of topological homes of this area and of comparable moduli areas, akin to the gap of actual algebraic curves, the distance of mappings, and likewise superanalogs of some of these areas.

Additional info for Advances on Fractional Inequalities

Example text

DJ; 8 ! J 2Œ0;R/ Ä K; 8 ! / d! N RN ! ˛ C N C 1/ à ˇ ˇ ds d! / d! / d! / d! / d! 37) So we have proved the Ostrowski inequality. 12. 0; R/ ! R be a Lebesgue integrable function, not necessarily radial. Assume f . Œ0; R/, R > 0; 8 ! 2 S N 1 I 0 < ˛ < 1; and DR˛ f . Œ0; R/, 8 ! t 2Œ0;R/ Ä K; 8 ! 2 S N 1 ; where K > 0. / d! 38) References 39 References 1. A. Anastassiou, Ostrowski type inequalities, Proc. AMS 123 (1995), 3775-3781. 2. A. Anastassiou, Fractional Differentiation Inequalities, Research Monograph, Springer, New York, 2009.

2. A. Anastassiou, Fractional Differentiation Inequalities, Research Monograph, Springer, New York, 2009. 3. A. Anastassiou, On Right Fractional Calculus, Chaos, Solitons and Fractals, 42 (2009), 365-376. 4. A. Anastassiou, Univariate right fractional Ostrowski inequalities, CUBO, accepted, 2011. 5. A. El-Sayed, M. Gaber, On the finite Caputo and finite Riesz derivatives, Electronic Journal of Theoretical Physics, Vol. 3, No. 12 (2006), 81-95. 6. S. M. Torres, Fractional Optimal Control in the sense of Caputo and the fractional Noether’s theorem, International Mathematical Forum, Vol.

24–26, we gave a complete theory of left fractional Ostrowski inequalities. Here we combine both right and left Caputo fractional derivatives and produce Ostrowski inequalities in the multivariate setting for radial functions. For the concepts of right and left Caputo fractional calculus we use here, we refer to [3–8, 12]. 3. 0; R/ WD fx 2 RN W jxj < Rg  RN ; N 2; R > 0 and the sphere SN 1 WD fx 2 RN W jxj D 1g; where j j is the Euclidean norm. Let d! be the element of surface measure on S N 1 and let Z 2 N=2 d!

Download PDF sample

Advances on Fractional Inequalities by George A. Anastassiou

by Charles

Rated 4.66 of 5 – based on 50 votes