Derivation of an amplitude of information in the setting of a new family of fractional entropies

Jumarie, Guy

doi:10.1016/j.ins.2012.06.008

Cited by 14 publications

(2 citation statements)

References 36 publications

(51 reference statements)

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“…We have proposed recently a fractional calculus based on fractional difference [9][10][11][12][13][14][15][16] which is slightly different from the classical Riemann-Liouville framework [1][2][3][4][5][6][20][21][22][23][24][25][26][27][28], and results in a useful fractional Taylor series [12] providing (2) as the first term. The fractional calculus so obtained is quite parallel to the classical calculus, and it involves non-commutative derivatives, what seems to be quite consistent with non commutative geometry.…”

Section: Purpose and Organization Of The Articlementioning

confidence: 99%

On the derivative chain-rules in fractional calculus via fractional difference and their application to systems modelling

Jumarie

2013

Open Physics

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Abstract:It has been pointed out that the derivative chains rules in fractional differential calculus via fractional calculus are not quite satisfactory as far as they can yield different results which depend upon how the formula is applied, that is to say depending upon where is the considered function and where is the function of function. The purpose of the present short note is to display some comments (which might be clarifying to some readers) on the matter. This feature is basically related to the non-commutativity of fractional derivative on the one hand, and furthermore, it is very close to the physical significance of the systems under consideration on the other hand, in such a manner that everything is right so. As an example, it is shown that the trivial first order system may have several fractional modelling depending upon the way by which it is observed. This suggests some rules to construct the fractional models of standard dynamical systems, in as meaningful a model as possible. It might happen that this pitfall comes from the feature that a function which is continuous everywhere, but is nowhere differentiable, exhibits random-like features. PACS

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Section: Purpose and Organization Of The Articlementioning

confidence: 99%

On the derivative chain-rules in fractional calculus via fractional difference and their application to systems modelling

Jumarie

2013

Open Physics

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“…We give some definitions and properties of the fractional calculus theory which are used further in this paper [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Exact and approximate solutions for the fractional Schrödinger equation with variable coefficients

Hong

Chen

2019

Adv Differ Equ

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In this paper, by introducing the fractional derivatives in the sense of Caputo, the modified general mapping deformation method (MGMDM) and the modified fractional variational iteration method (MFVIM) are applied to obtain some exact and approximate solutions of the variable-coefficient fractional Schrödinger equation (VFNLS) with time and space fractional derivatives. With the aid of symbolic computation, a broad class of exact analytical solutions and their structure of the VFNLS are investigated. Furthermore, the approximate iterative series showed that the MFVIM is powerful, reliable and effective when compared with some traditional decomposition method in searching for the approximate solutions of the complex nonlinear partial differential equations with variable coefficients and fractional derivatives.

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Financial Modelling and Memory: Mathematical System

Tapiero

Vallois

2014

International Series in Operations Research &Amp; Management Science

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Derivation of an amplitude of information in the setting of a new family of fractional entropies

Cited by 14 publications

References 36 publications

On the derivative chain-rules in fractional calculus via fractional difference and their application to systems modelling

On the derivative chain-rules in fractional calculus via fractional difference and their application to systems modelling

Exact and approximate solutions for the fractional Schrödinger equation with variable coefficients

Financial Modelling and Memory: Mathematical System

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