Results 61 to 70 of about 14,096 (164)
Analysis of linear continuous-time systems by the use of the conformable fractional calculus and Caputo [PDF]
Archives of Electrical Engineering, 2018 The paper presents general solutions for fractional state-space equations. The analysis of the fractional electrical circuit in the transient state is described by the equation of the state and space equations.
Ewa Piotrowska
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Fractional Herglotz variational principles with generalized Caputo derivatives [PDF]
Chaos, Solitons & Fractals, 2017 We obtain Euler-Lagrange equations, transversality conditions and a Noether-like theorem for Herglotz-type variational problems with Lagrangians depending on generalized fractional derivatives. As an application, we consider a damped harmonic oscillator with time-depending mass and elasticity, and arbitrary memory effects.
Garra R., Taverna G. S., Torres D. F. M.
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Nonlinear Analysis, 2012 Fractional derivative equations account for relaxation and diffusion processes in a large variety of condensed matter systems. For instance, diffusion of position probability density displayed by a random walker in complex systems – such as glassy ...
Arnaud Heibig, Liviu Iulian Palade
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AIP AdvancesFractal-fractional derivatives are more general than the fractional derivative and classical derivative in terms of order. Fractal-fractional derivative is used in those models where the classical continuum hypothesis theory fails.
Saqib Murtaza +7 more
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Generalized Schwarzian derivatives for generalized fractional linear transformations [PDF]
Annales Polonici Mathematici, 1992 The classical Schwarzian derivative \((w'''/w')-(3/2)(w''/w')^ 2\) in the complex plane is generalized to \(\mathbb{R}^ n\) by using a Clifford algebra structure. The author presents properties of his Schwarzian derivative and characterizes local diffeomorphisms \(w:\mathbb{R}^ n\to\mathbb{R}^ n\) with vanishing Schwarzian.
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Axioms, 2015 This article is in continuation of the authors research attempts to derive computational solutions of an unified reaction-diffusion equation of distributed order associated with Caputo derivatives as the time-derivative and Riesz-Feller derivative as ...
Ram K. Saxena +2 more
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Abstract and Applied Analysis, 2013 The one-dimensional heat equations with the heat generation arising in fractal transient conduction associated with local fractional derivative operators are investigated.
Ai-Ming Yang +3 more
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A New Approach to Generalized Fractional Derivatives
, 2011 The author \mbox{(Appl. Math. Comput. 218(3):860-865, 2011)} introduced a new fractional integral operator given by, \[ \big({}^ρ\mathcal{I}^α_{a+}f\big)(x) = \frac{ρ^{1- α}}{Γ(α)} \int^x_a \frac{τ^{ρ-1} f(τ) }{(x^ρ- τ^ρ)^{1-α}}\, dτ, \] which generalizes the well-known Riemann-Liouville and the Hadamard fractional integrals. In this paper we present a
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On Generalized k-Fractional Derivative Operator
, 2017 The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to k-hypergeometric and k-Appell's functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler
Gauhar Rahman +2 more
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Generalized Brouncker’s continued fractions and their logarithmic derivatives [PDF]
The Ramanujan Journal, 2013 In this paper, we study the continued fraction y(s,r) which satisfies the equation y(s,r)y(s+2r,r)=(s+1)(s+2r-1) for r > 1/2. This continued fraction is a generalization of the Brouncker's continued fraction b(s). We extend the formulas for the first and the second logarithmic derivatives of b(s) to the case of y(s,r).
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