Details

Advances on Fractional Inequalities


Advances on Fractional Inequalities


SpringerBriefs in Mathematics

von: George A. Anastassiou

50,28 €

Verlag: Springer
Format: PDF
Veröffentl.: 25.07.2011
ISBN/EAN: 9781461407034
Sprache: englisch
Anzahl Seiten: 122

Dieses eBook enthält ein Wasserzeichen.

Beschreibungen

<p>Advances on Fractional Inequalities  use primarily the Caputo fractional derivative, as the most important in applications, and presents the first fractional differentiation inequalities of Opial type which  involves the balanced fractional derivatives. The book continues with right and mixed fractional differentiation Ostrowski inequalities in the univariate and multivariate cases. Next the right and left, as well as mixed, Landau fractional differentiation inequalities in the univariate and multivariate cases are illustrated. Throughout the book many applications are given. </p><p>Fractional differentiation inequalities are by themselves an important and great mathematical topic for research. Furthermore they have many applications, the most important ones are in establishing uniqueness of solution in fractional differential equations and systems and in fractional partial differential equations. Also they provide upper bounds to the solutions of the above equations.</p><p>Fractional Calculus has emerged as very useful over the last forty years due to its many applications in almost all applied sciences. This is currently seen in applications in acoustic wave propagation in inhomogeneous porous material, diffusive transport, fluid flow, dynamical processes in self-similar structures, dynamics of earthquakes, optics, geology, viscoelastic materials, bio-sciences, bioengineering, medicine, economics, probability and statistics, astrophysics, chemical engineering, physics, splines, tomography, fluid mechanics, electromagnetic waves, nonlinear control, signal processing, control of power electronic, converters, chaotic dynamics, polymer science, proteins, polymer physics, electrochemistry, statistical physics, rheology, thermodynamics, neural networks, etc. Almost all fields of research in science and engineering use fractional calculus in order to describe results.</p><p>This book is a part of Fractional Calculus, therefore it  is useful for researchersand graduate students for research, seminars and advanced graduate courses, in pure and applied mathematics, engineering and all other applied sciences.</p>
<p>-1. Opial-type inequalities for balanced fractional derivatives(Introduction, Background, Main Results, References). -2. Univariate right Caputo fractional Ostrowski inequalities (Introduction, Main Results, References). -3. Multivariate right Caputo fractional Ostrowski inequalities (Introduction, Main Results, References).-4. Univariate mixed fractional Ostrowski inequalities (Introduction, Main Results, References).-5. Multivariate radical mixed fractional Ostrowski inequalities(Introduction, Main Results, References).-6. Shell mixed Caputo fractional Ostrowski inequalities(Introduction, Main Results, References).-7. Left Caputo fractional uniform Landau inequalities (Introduction, Main Results, References).-8. Left Caputo Fractional Landau type Inequalities(Introduction, Main Results, References).-9. Right Caputo Fractional Landau type Inequalities(Introduction, Main Results, References).-10. Mixed Caputo Fractional Landau type Inequalities(Introduction, Main Results, References).-11. Multivariate Caputo Fractional Landau type Inequalities(Introduction, Main Results, References).</p>
Use primarily the Caputo fractional derivative, as the most important in applications, and we present first fractional differentiation inequalities of Opial type where we involve the so called balanced fractional derivatives Fractional differentiation inequalities have many applications, the most important ones are in establishing uniqueness of solution in fractional differential equations and systems and in fractional partial differential equations. Also they provide upper bounds to the solutions of the above equations Fractional Calculus has applications in acoustic wave propagation in homogeneous porous material, diffusive transport, fluid flow, earthquakes, optics, geology, viscoelastic materials, bio-sciences, dynamical processes in self-similar structures, dynamics of bioengineering, medicine, economics, probability and statistics, astrophysics, chemical engineering, physics, splines, tomography, fluid mechanics, electromagnetic waves, nonlinear control, signal processing, control of power electronic, converters, chaotic dynamics, polymer science, proteins, polymer physics, electrochemistry, statistical physics, rheology, thermodynamics, neural networks, etc Includes supplementary material: sn.pub/extras

Diese Produkte könnten Sie auch interessieren:

Classical Fourier Analysis
Classical Fourier Analysis
von: Loukas Grafakos
PDF ebook
50,24 €
Nonsmooth Dynamics of Contacting Thermoelastic Bodies
Nonsmooth Dynamics of Contacting Thermoelastic Bodies
von: Jan Awrejcewicz, Yuriy Pyr'yev
PDF ebook
106,99 €
Introduction to Hamiltonian Dynamical Systems and the N-Body Problem
Introduction to Hamiltonian Dynamical Systems and the N-Body Problem
von: Kenneth Meyer, Glen Hall, Dan Offin
PDF ebook
106,99 €