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  • 1
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    The Vertical Linear Fractional Initialization Problem (1999)
    In:  CASI
    Details
    Publikationsdatum: 2019-07-10
    Beschreibung: This paper presents a solution to the initialization problem for a system of linear fractional-order differential equations. The scalar problem is considered first, and solutions are obtained both generally and for a specific initialization. Next the vector fractional order differential equation is considered. In this case, the solution is obtained in the form of matrix F-functions. Some control implications of the vector case are discussed. The suggested method of problem solution is shown via an example.
    Schlagwort(e): Mathematical and Computer Sciences (General)
    Materialart: NASA/TP-1999-208919 , NAS 1.60:208919 , E-11699
    Format: application/pdf
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  • 2
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    A Solution to the Fundamental Linear Fractional Order Differential Equation (1998)
    In:  CASI
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    Publikationsdatum: 2019-07-10
    Beschreibung: This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.
    Schlagwort(e): Mathematical and Computer Sciences (General)
    Materialart: NASA/TP-1998-208693 , E-11408 , NAS 1.60:208693
    Format: application/pdf
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  • 3
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    Intitialization, Conceptualization, and Application in the Generalized Fractional Calculus (1998)
    In:  CASI
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    Publikationsdatum: 2019-07-10
    Beschreibung: This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set of definitions for the fractional calculus is provided which formally include the effects of initialization. Conceptualizations of fractional derivatives and integrals are shown. Physical examples of the basic elements from electronics are presented along with examples from dynamics, material science, viscoelasticity, filtering, instrumentation, and electrochemistry to indicate the broad application of the theory and to demonstrate the use of the mathematics. The fundamental criteria for a generalized calculus established by Ross (1974) are shown to hold for the generalized fractional calculus under appropriate conditions. A new generalized form for the Laplace transform of the generalized differintegral is derived. The concept of a variable structure (order) differintegral is presented along with initial efforts toward meaningful definitions.
    Schlagwort(e): Mathematical and Computer Sciences (General)
    Materialart: NASA/TP-1998-208415 , E-11241 , NAS 1.60:208415
    Format: application/pdf
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  • 4
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    Insights Into the Fractional Order Initial Value Problem via Semi-Infinite Systems (1998)
    In:  CASI
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    Publikationsdatum: 2019-07-10
    Beschreibung: This paper considers various aspects of the initial value problem for fractional order differential equations. The main contribution of this paper is to use the solutions to known spatially distributed systems to demonstrate that fractional differintegral operators require an initial condition term that is time-varying due to past distributed storage of information.
    Schlagwort(e): Mathematical and Computer Sciences (General)
    Materialart: NASA/TM-1998-208407 , E-11242 , NAS 1.15:208407
    Format: application/pdf
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