• Title/Summary/Keyword: fractional calculus

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Innovative modeling of tuned liquid column damper controlled structures

  • Di Matteo, Alberto;Di Paola, Mario;Pirrotta, Antonina
    • Smart Structures and Systems
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    • v.18 no.1
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    • pp.117-138
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    • 2016
  • In this paper a different formulation for the response of structural systems controlled by Tuned Liquid Column Damper (TLCD) devices is developed, based on the mathematical tool of fractional calculus. Although the increasing use of these devices for structural vibration control, it has been demonstrated that existing model may lead to inaccurate prediction of liquid motion, thus reflecting in a possible imprecise description of the structural response. For this reason the recently proposed fractional formulation introduced to model liquid displacements in TLCD devices, is here extended to deal with TLCD controlled structures under base excitations. As demonstrated through an extensive experimental analysis, the proposed model can accurately capture structural responses both in time and in frequency domain. Further, the proposed fractional formulation is linear, hence making identification of the involved parameters extremely easier.

Fractional order generalized thermoelastic study in orthotropic medium of type GN-III

  • Lata, Parveen;Zakhmi, Himanshi
    • Geomechanics and Engineering
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    • v.19 no.4
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    • pp.295-305
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    • 2019
  • The present paper is concerned with the investigation of disturbances in orthotropic thermoelastic medium by using fractional order heat conduction equation with three phase lags due to thermomechanical sources. Laplace and Fourier transform techniques are used to solve the problem. The expressions for displacement components, stress components and temperature change are derived in transformed domain and further in physical domain using numerical inversion techniques. The effect of fractional parameter based on its conductivity i.e., ($0<{\alpha}<1$ for weak, ${\alpha}=1$ for normal, $1<{\alpha}{\leq}2$ for strong conductivity) is depicted graphically on various components.

Stability analysis in BWRs with double subdiffusion effects: Reduced order fractional model (DS-F-ROM)

  • Gilberto Espinosa-Paredes;Ricardo I. Cazares-Ramirez;Vishwesh A. Vyawahare;Erick-G. Espinosa-Martinez
    • Nuclear Engineering and Technology
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    • v.56 no.4
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    • pp.1296-1309
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    • 2024
  • The aim of this work is to explore the effect of the double subdiffusion on the stability in BWRs. A BWR novel reduced order model with double subdiffusion effects: reduced order fractional model (DS-F-ROM) to describe the neutron and heat transfer processes was proposed for this study. The double subdiffusion was developed with a fractional-order two-equation model, and with different fractional-orders and relaxation times. The stability analysis was carried out using the root-locus method and change from the s to the W domain and were confirmed using the time-domain evolution of neutron flux for a unit step change in reactivity. The results obtained using the reduced fractional-order model are presented for different anomalous diffusion coefficient values. Results are compared with normal diffusion and P1 equations, which are obtained straightforwardly with DS-ROM when relaxation time tends to zero, and when the anomalous diffusion coefficient tends to one, respectively.

ON SUBCLASSES OF UNIVALENT FUNCTIONS WITH NEGATIVE COEFFICIENTS

  • Altintas, Osman;Owa, Shigeyoshi
    • East Asian mathematical journal
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    • v.4
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    • pp.41-56
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    • 1988
  • In this work we obtain inequalities for coefficients related to functions belonging to two subclasses of univalent functions with negative coefficients, bounds for the modulus of these functions and their derivatives, and the extreme points of these classes. We also show an application of functions belonging to these classes to the fractional calculus.

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A REMARK ON NEW CRITERIA FOR UNIVALENT FUNCTIONS

  • Owa, Shigeyoshi
    • Kyungpook Mathematical Journal
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    • v.21 no.1
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    • pp.15-23
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    • 1981
  • St. Ruscheweyh suggested new criteria for univalent functions and two problems. In this paper, we shall give the relation between new criteria and fractional calculus and some results for Ruscheweyh's problems in a sense.

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THE INCOMPLETE GENERALIZED τ-HYPERGEOMETRIC AND SECOND τ-APPELL FUNCTIONS

  • Parmar, Rakesh Kumar;Saxena, Ram Kishore
    • Journal of the Korean Mathematical Society
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    • v.53 no.2
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    • pp.363-379
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    • 2016
  • Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [Integral Transforms Spec. Funct. 23 (2012), 659-683] and the second Appell function [Appl. Math. Comput. 219 (2013), 8332-8337] by means of the incomplete Pochhammer symbols $({\lambda};{\kappa})_{\nu}$ and $[{\lambda};{\kappa}]_{\nu}$, we introduce here the family of the incomplete generalized ${\tau}$-hypergeometric functions $2{\gamma}_1^{\tau}(z)$ and $2{\Gamma}_1^{\tau}(z)$. The main object of this paper is to study these extensions and investigate their several properties including, for example, their integral representations, derivative formulas, Euler-Beta transform and associated with certain fractional calculus operators. Further, we introduce and investigate the family of incomplete second ${\tau}$-Appell hypergeometric functions ${\Gamma}_2^{{\tau}_1,{\tau}_2}$ and ${\gamma}_2^{{\tau}_1,{\tau}_2}$ of two variables. Relevant connections of certain special cases of the main results presented here with some known identities are also pointed out.

Time harmonic interactions in an orthotropic media in the context of fractional order theory of thermoelasticity

  • Lata, Parveen;Zakhmi, Himanshi
    • Structural Engineering and Mechanics
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    • v.73 no.6
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    • pp.725-735
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    • 2020
  • The present investigation deals with the thermomechanical interactions in an orthotropic thermoelastic homogeneous body in the context of fractional order theory of thermoelasticity due to time harmonic sources. The application of a time harmonic concentrated and distributed sources has been considered to show the utility of the solution obtained. Assuming the disturbances to be harmonically time dependent, the expressions for displacement components, stress components and temperature change are derived in frequency domain. Numerical inversion technique has been used to determine the results in physical domain. The effect of frequency on various components has been depicted through graphs.

FRACTIONAL INTEGRATION AND DIFFERENTIATION OF THE (p, q)-EXTENDED BESSEL FUNCTION

  • Choi, Junesang;Parmar, Rakesh K.
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.2
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    • pp.599-610
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    • 2018
  • We aim to present some formulas for Saigo hypergeometric fractional integral and differential operators involving (p, q)-extended Bessel function $J_{{\nu},p,q}(z)$, which are expressed in terms of Hadamard product of the (p, q)-extended Gauss hypergeometric function and the Fox-Wright function $_p{\Psi}_q(z)$. A number of interesting special cases of our main results are also considered. Further, it is emphasized that the results presented here, which are seemingly complicated series, can reveal their involved properties via those of the two known functions in their respective Hadamard product.

On a Class of Spirallike Functions associated with a Fractional Calculus Operator

  • SELVAKUMARAN, KUPPATHAI APPASAMY;BALACHANDAR, GEETHA;RAJAGURU, PUGAZHENTHI
    • Kyungpook Mathematical Journal
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    • v.55 no.4
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    • pp.953-967
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    • 2015
  • In this article, by making use of a linear multiplier fractional differential operator $D^{{\delta},m}_{\lambda}$, we introduce a new subclass of spiral-like functions. The main object is to provide some subordination results for functions in this class. We also find sufficient conditions for a function to be in the class and derive Fekete-$Szeg{\ddot{o}}$ inequalities.