On conformable delta fractional calculus on time scales

Zhao, Dafang; Li, Tongxing

doi:10.22436/jmcs.016.03.03

Cited by 30 publications

(26 citation statements)

References 7 publications

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“…Unfortunately, that is a matter beyond the scope of this work, cf. [19,[23][24][25][26]. Henceforth and for the sake of politeness, we use the word "operator" instead of "derivative" to refer to the fractional conformable definition.…”

Section: Introductionmentioning

confidence: 99%

Entropy Generation in a Mass-Spring-Damper System Using a Conformable Model

2020

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This article studies the entropy generation of a mass-spring-damper mechanical system, under the conformable fractional operator definition. We perform several simulations by varying the fractional order γ and the damping ratio ζ , including the usual dynamic response when γ = 1.0 and the typical damping cases. We analyze the entropy production for this system and its strong dependency on both γ and ζ parameters. Therefore, we determine their optimal values to obtain the highest efficiency of the MSD response, as well as other impressive features.

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Section: Introductionmentioning

confidence: 99%

Entropy Generation in a Mass-Spring-Damper System Using a Conformable Model

2020

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“…Karayer et al [20] introduced the conformable fractional Nikiforov-Uvarov (NU) method for some prospect in quantum mechanics which gives accurate Eigen case solutions of Schrodinger equation (SE). Zhao et al [21] discuss a new connotation of the delta conformable fractional derivative which has the identity factor on time scales. In, Ünal et al [22] evidenced the power series solutions about given point in case of conformable fractional differential equations of linear sequential homogeneous of order 2α and introduced the Hermite conformable fractional polynomials as well as the basic properties of these polynomials.…”

Section: Brief Introduction On Fractional Calculusmentioning

confidence: 99%

Studying the fractional derivative for natural convection in slanted cavity containing porous media

et al. 2019

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This paper studies the numerical solution of the unsteady free convention in a slanted cavity under effect of the fractional derivative containing a porous medium. To simplify all the computations, the main equations are mapped from the irregular physical domain into a regular polygon in a shape of a rectangular computational domain utilizing nonlinear axis transformations. Using the finite differences method, the fractional partial differential equations are solved. The primary results are teased in the ordinary case at = 1, Ra = 1000 and = 0.0 and those are found in an excellent agreement with the previous results from the open literatures. The obtained numerical data are represented in terms of the isotherms and streamlines contours as well as the local and average Nusselt numbers at the heated wall. Wide ranges of the key-parameters are considered i.e. orders of the fractional derivatives and are varied from 1 to 0.7, the Rayleigh number Ra is varied from 10 2 to 10 4 and the inclination angle takes the values = 0 • , 15 • , 30 • and 45•

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“…However, properties, such as the product rule, quotient rule, chain rule, Rolle theorem, mean value theorem, and composition rule, are lacking in almost all fractional derivatives. [27][28][29][30][31] Motivated by this new conformable derivative, we apply it to the well-known series RC, LC, and RLC electric circuits and analyse their behaviour. To avoid these difficulties, in Khalil et al, 24 it was proposed an interesting idea that extends the ordinary limit definitions of the derivatives of a function called conformable fractional derivative.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, there is a large number of works carried out using this new definition. [27][28][29][30][31] Motivated by this new conformable derivative, we apply it to the well-known series RC, LC, and RLC electric circuits and analyse their behaviour. The solutions depend on time and on the fractional order parameter 0 < γ ≤ 1.…”

Section: Introductionmentioning

confidence: 99%

Electrical circuits described by fractional conformable derivative

López-Martínez

Rosales

Carreño

et al. 2018

Circuit Theory & Apps

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Summary In the last 3 years, the fractional conformable derivative and its properties have been introduced. Unlike other definitions, this new fractional derivative is based on the basic limit definition of the derivative and satisfies the same formulas of derivation, such as product and quotient of 2 functions and the chain rule. Using this new derivative, we obtain a new class of linear ordinary differential equations with noninteger power variable coefficients for the Resistance Capacitance (RC), Inductance Capacitance (LC), and Resistance, Inductance Capacitance (RLC) electric circuits. The numerical solutions are solved through the Matlab software. Solutions depend on time and on the fractional order parameter 0 < γ ≤ 1. The computing using this new derivative is much easier than using other definitions of fractional derivative. It has been shown that in the particular case γ = 1, these solutions become the ordinary ones. Also, a comparison has been made with the Caputo fractional derivative for the case of the RC circuit with constant source.

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On conformable delta fractional calculus on time scales

Abstract: In this paper, we introduce and investigate the concepts of conformable delta fractional derivative and conformable delta fractional integral on time scales. Basic properties of the theory are proved.

Cited by 30 publications

References 7 publications

Entropy Generation in a Mass-Spring-Damper System Using a Conformable Model

Entropy Generation in a Mass-Spring-Damper System Using a Conformable Model

Studying the fractional derivative for natural convection in slanted cavity containing porous media

Electrical circuits described by fractional conformable derivative

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