A Numerical Scheme for Dynamic Systems Containing Fractional Derivatives

By Lixia Yuan, Om Prakash Agrawal. 2002

276 citations recorded by the source corpus.

Subfields: Mechanics of Materials, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/f958093ed3ab98ee0baf246429e385971a73ac98

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In Mechanics of Materials

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Galerkin Projections and Finite Elements for Fractional Order Derivatives (2006, methodology): “In this paper, however, we go beyond the treatment of [ 16 ] and develop a Galerkin projection as well as finite elements for the dimensional reduction; in this way, we are able to provide a clearer picture of the performance and accuracy of the method.”
An improved non-classical method for the solution of fractional differential equations (2010, methodology): “It should be noted that Eq. (9) is also obtained applying the Laplace transformation to the time-domain definition of the fractional derivative derived in [13,14, 29 ,32] and given in the Appendix, Eq. (68).”
Invariant analysis of time fractional generalized Burgers and Korteweg–de Vries equations (2012, background): “and other numerical schemes [22,23] have been formulated.”
Fractional optimal control problems: a pseudo-state-space approach (2011, background): “Lixia and Agrawal (2002) propose an infinite dimensional state-space realization of a fractional derivative where the fractional dynamical equation is transformed into a set of differential equations with no fractional derivative terms and Laguerre integral formula is used to convert this set of…”
Numerical Approaches to Fractional Integrals and Derivatives: A Review (2020, background): “Alternatively, other literatures have regarded g(z, x) as the solution of a first order ordinary differential (ODE) equation [52,53,58,59],”
A Lyapunov approach to the stability of fractional differential equations (2009, background): “This state space model (23), (24) and closely related concepts have been discussed by a number of authors before: refer to the survey paper by Diethelm [6] and the references cited there, in particular the works of Chatterjee [4] and Yuan and Agrawal [24].”
Optimality conditions and a solution scheme for fractional optimal control problems (2009, background): “Expressions (19), (21) for the fractional derivatives are of the type used earlier (not for optimization) by Yuan and Agrawal (1998, 2002) and Ruge and Trinks (2004).”
Treatment of dynamic systems with fractional derivatives without evaluating memory-integrals (2002, methodology): “Nevertheless, it will be profitable to use the scheme proposed by Yuan and Agrawal (2002) for 0 < a < 1 and generalized for 1 < a < 2 in this paper when dealing with longer observation times.”