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Full-Text Articles in Physical Sciences and Mathematics
Recent Applications Of Fractional Calculus To Science And Engineering, Lokenath Debnath
Recent Applications Of Fractional Calculus To Science And Engineering, Lokenath Debnath
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
This paper deals with recent applications of fractional calculus to dynamical systems in control theory, electrical circuits with fractance, generalized voltage divider, viscoelasticity, fractional-order multipoles in electromagnetism, electrochemistry, tracer in fluid flows, and model of neurons in biology. Special attention is given to numerical computation of fractional derivatives and integrals.
Category Of Nonlinear Evolution Equations, Algebraic Structure, And R-Matrix, Zhijun Qiao, Cewen Cao, Walter Strampp
Category Of Nonlinear Evolution Equations, Algebraic Structure, And R-Matrix, Zhijun Qiao, Cewen Cao, Walter Strampp
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
In this paper we deal with the category of nonlinear evolution equations ~NLEEs! associated with the spectral problem and provide an approach for constructing their algebraic structure and r-matrix. First we introduce the category of NLEEs, which is composed of various positive order and negative order hierarchies of NLEEs both integrable and nonintegrable. The whole category of NLEEs possesses a generalized Lax representation. Next, we present two different Lie algebraic structures of the Lax operator: one of them is universal in the category, i.e., independent of the hierarchy, while the other one is nonuniversal in the hierarchy, i.e., dependent on …