scholarly journals The $\mathbb{N}_0$ Story: Discrete Fractional Calculus

2022 ◽  
Vol 69 (02) ◽  
pp. 1
Author(s):  
Raegan Higgins ◽  
Heidi Berger
Keyword(s):  
Fractional Calculus ◽  
Discrete Fractional Calculus

Discrete Fractional Diffusion Equation of Chaotic Order

2016 ◽  
Vol 26 (01) ◽  
pp. 1650013 ◽  
Author(s):  
Guo-Cheng Wu ◽  
Dumitru Baleanu ◽  
He-Ping Xie ◽  
Sheng-Da Zeng
Keyword(s):  
Porous Media ◽  
Fractional Calculus ◽  
Diffusion Equation ◽  
Discrete Time ◽  
Chaotic Map ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Variable Order ◽  
Diffusion Modeling ◽  
Discrete Fractional Calculus

Discrete fractional calculus is suggested in diffusion modeling in porous media. A variable-order fractional diffusion equation is proposed on discrete time scales. A function of the variable order is constructed by a chaotic map. The model shows some new random behaviors in comparison with other variable-order cases.

scholarly journals Some Hardy-Type Inequalities for Superquadratic Functions via Delta Fractional Integrals

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Usama Hanif ◽  
Ammara Nosheen ◽  
Rabia Bibi ◽  
Khuram Ali Khan ◽  
Hamid Reza Moradi
Keyword(s):  
Fractional Calculus ◽  
Time Scales ◽  
Fractional Integrals ◽  
Discrete Fractional Calculus ◽  
Hardy Inequalities ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Superquadratic Functions

In this paper, Jensen and Hardy inequalities, including Pólya–Knopp type inequalities for superquadratic functions, are extended using Riemann–Liouville delta fractional integrals. Furthermore, some inequalities are proved by using special kernels. Particular cases of obtained inequalities give us the results on time scales calculus, fractional calculus, discrete fractional calculus, and quantum fractional calculus.

A New Insight Into the Grünwald–Letnikov Discrete Fractional Calculus

2019 ◽  
Vol 14 (4) ◽  
Author(s):  
Yiheng Wei ◽  
Weidi Yin ◽  
Yanting Zhao ◽  
Yong Wang
Keyword(s):  
Fractional Calculus ◽  
Discrete Fractional Calculus ◽  
Fractional Difference ◽  
Integer Order ◽  
Convolution Operation ◽  
Order Case ◽  
Insight Into

The primary work of this paper is to investigate some potential properties of Grünwald–Letnikov discrete fractional calculus. By employing a concise and convenient description, this paper not only establishes excellent relationships between fractional difference/sum and the integer order case but also generalizes the Z-transform and convolution operation.

scholarly journals Bayesian Estimation in Delta and Nabla Discrete Fractional Weibull Distributions

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
M. Ganji ◽  
F. Gharari
Keyword(s):  
Fractional Calculus ◽  
Bayesian Estimation ◽  
Time Scales ◽  
Discrete Distributions ◽  
Weibull Distributions ◽  
Discrete Fractional Calculus

We use discrete fractional calculus for showing the existence of delta and nabla discrete distributions and then apply time scales for definitions of delta and nabla discrete fractional Weibull distributions. Also, we study the Bayesian estimation of the functions of parameters of these distributions.

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