Physical and geometrical interpretation of fractional operators

Moshrefi-Torbati, M.; Hammond, J.K.

doi:10.1016/s0016-0032(97)00048-3

Cited by 128 publications

(56 citation statements)

References 5 publications

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“…The parameter σ (auxiliary parameter) represents the fractional time components in the system, components that show an intermediate behavior between a system conservative and dissipative. The physical and geometrical interpretation of the fractional operators is given in [39]- [40].…”

Section: Fractional Rlc Circuitmentioning

confidence: 99%

RLC electrical circuit of non-integer order

2013

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Abstract:In this work a fractional differential equation for the electrical RLC circuit is studied. The order of the derivative being considered is 0 < γ ≤ 1. To keep the dimensionality of the physical quantities R L and C an auxiliary parameter σ is introduced. This parameter characterizes the existence of fractional components in the system. It is shown that there is a relation between γ and σ through the physical parameters RLC of the circuit. Due to this relation, the analytical solution is given in terms of the Mittag-Leffler function depending on the order γ of the fractional differential equation.PACS (2008)

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Section: Fractional Rlc Circuitmentioning

confidence: 99%

RLC electrical circuit of non-integer order

2013

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“…The distinct formulations of fractional derivatives and integrals lead to several proposals for the interpretation of the generalized operator [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54]. In spite of this diversity it is clear that FODS require an initialization procedure taking into account the history of the dynamical phenomenon that is not asked for in the classical integer order approach.…”

Section: Fundamental Conceptsmentioning

confidence: 99%

Numerical analysis of the initial conditions in fractional systems

Machado

2014

Communications in Nonlinear Science and Numerical Simulation

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a b s t r a c tFractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.

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“…al. considered the Riemman-Lioville fractional derivative of a function as the convolution of this function with a kernel (h∞) [18]. Molz et.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Velocity and Fuzzy Acceleration in Fractional Order Motion

Ateş¹,

Alagöz²,

Alisoy³

et al. 2015

Balkan Journal of Electrical and Computer Engineering

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Fractional calculus presents a new perspective for solution of scientific and engineering problems. There are still many fields where fractional calculus promise fresh understanding of real world problems. In this study, we present an investigation on fractional order motion, where we extend our comprehension from velocity and acceleration concepts to a fuzzy velocity and acceleration domains. Here, fundamentally, we suggest a debate on interpretation of fractional-order derivative system on the bases of integer-order derivative knowledge. We observed that the continuous fractional-order motion equation set can be considered to cover the discrete integer-order motion equation set and physical meaning of fractional-order motion systems can be better understood by using a fuzzy conceptualization of integer-order derivative systems according to the dissimilarity metric.

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Physical and geometrical interpretation of fractional operators

Cited by 128 publications

References 5 publications

RLC electrical circuit of non-integer order

RLC electrical circuit of non-integer order

Numerical analysis of the initial conditions in fractional systems

Fuzzy Velocity and Fuzzy Acceleration in Fractional Order Motion

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