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Journal ArticleDOI

Applications of Fractional Calculus to Dynamic Problems of Linear and Nonlinear Hereditary Mechanics of Solids

Yuriy A. Rossikhin, +1 more
- 01 Jan 1997 - 
- Vol. 50, Iss: 1, pp 15-67
About: 
This article is published in Applied Mechanics Reviews.The article was published on 1997-01-01. It has received 681 citations till now. The article focuses on the topics: Fractional calculus & Elasticity (economics).

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Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics

Francesco Mainardi
- 01 Jan 2001 - 
TL;DR: In this article, the authors review some applications of fractional calculus developed by the author (partly in collaboration with others) to treat some basic problems in continuum and statistical mechanics.
Journal ArticleDOI

A new operational matrix for solving fractional-order differential equations

Abbas Saadatmandi, +1 more
- 01 Feb 2010 - 
TL;DR: The main aim is to generalize the Legendre operational matrix to the fractional calculus and reduces such problems to those of solving a system of algebraic equations thus greatly simplifying the problem.
Journal ArticleDOI

A General Formulation and Solution Scheme for Fractional Optimal Control Problems

Om P. Agrawal
- 01 Dec 2004 - 
TL;DR: In this article, a general formulation and a solution scheme for a class of Fractional Optimal Control Problems (FOCPs) for those systems are presented, where the performance index of a FOCP is considered as a function of both the state and the control variables, and the dynamic constraints are expressed by a set of FDEs.
Journal ArticleDOI

Application of Fractional Calculus for Dynamic Problems of Solid Mechanics: Novel Trends and Recent Results

Yuriy A. Rossikhin, +1 more
- 01 Jan 2010 - 
TL;DR: In this article, the authors present the analysis of new trends and recent results carried out during the last 10 years in the field of fractional calculus application to dynamic problems of solid mechanics.
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Fractional heat conduction equation and associated thermal stress

Yuriy Povstenko
- 15 Dec 2004 - 
TL;DR: A quasi-static uncoupled theory of thermoelasticity based on the heat conduction equation with a time-fractional derivative of order α is proposed in this article.
References
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Journal ArticleDOI

Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics

Kenneth S. Cole, +1 more
- 01 Apr 1941 - 
TL;DR: In this paper, the locus of the dielectric constant in the complex plane was defined to be a circular arc with end points on the axis of reals and center below this axis.
Book

An Introduction to the Fractional Calculus and Fractional Differential Equations

Kenneth S. Miller, +1 more
TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.
Journal ArticleDOI

Linear Models of Dissipation whose Q is almost Frequency Independent-II

Michele Caputo
- 01 Nov 1967 - 
TL;DR: In this paper, a linear dissipative mechanism whose Q is almost frequency independent over large frequency ranges has been investigated by introducing fractional derivatives in the stressstrain relation, and a rigorous proof of the formulae to be used in obtaining the analytic expression of Q is given.
Book

Solitons and Nonlinear Wave Equations

R. K. Dodd, +3 more
TL;DR: A discussion of the theory and applications of classical solitons is presented in this paper with a brief treatment of quantum mechanical effects which occur in particle physics and quantum field theory, including solitary waves and soliton, scattering transforms, the Schroedinger equation and the Korteweg-de Vries equation.
Journal ArticleDOI

A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity

Ronald L. Bagley, +1 more
- 01 Jun 1983 - 
TL;DR: In this article, the authors established a link between molecular theories that predict the macroscopic behavior of certain viscoelastic media and an empirically developed fractional calculus approach to visco-elasticity.