Restricted fractional differential transform for solving irrational order fractional differential equations

Khudair, Ayad R.; Haddad, S. A. M.; Khalaf, Sanaa L.

doi:10.1016/j.chaos.2017.05.026

Cited by 24 publications

(11 citation statements)

References 31 publications

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“…Fractional differentiation is an extension of integer-order differentiation, which is used to study the mathematical properties and applications of differential mathematics of any order [ 41 ]. The fractional differential of Grunwald–Letnikov [ 42 ] is as follows:

where α is differential order, h is differential step length, Г is a gamma function, q is a real number, f ( x ) is a one-dimensional signal, t is a time variable of a one-dimensional signal, m ∈ Z , Z is a set of integers.…”

Section: Experimental Data and Preprocessingmentioning

confidence: 99%

Dropout Deep Belief Network Based Chinese Ancient Ceramic Non-Destructive Identification

Huang

Guan

2021

Sensors

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A non-destructive identification method was developed here based on dropout deep belief network in multi-spectral data of ancient ceramic. A fractional differential algorithm was proposed to enhance the spectral details by making use of the difference between the first and second-order differential pre-process spectral data. An unsupervised multi-layer restricted Boltzmann machine (RBM) was employed to extract some high-level features during pre-training. Some weight and bias values trained by RBM were used to initialize a back propagation (BP) neural network. The RBM deep belief network was fine-tuned by the BP neural network to promote the initiative performance of network training, which helped to overcome local optimal limitation of the network due to the random initializing weight parameter. The dropout strategy has been put forward into the RBM network to solve the over-fitting of small sample spectral data. The experimental results show that the proposed method has excellent recognition performance of the ceramics by comparisons with some other ones.

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Section: Experimental Data and Preprocessingmentioning

confidence: 99%

Dropout Deep Belief Network Based Chinese Ancient Ceramic Non-Destructive Identification

Huang

Guan

2021

Sensors

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“…Remark [37] R-LF derivative and CF derivative have the following relationship: ). nc/4.0/ -http://creativecommons.org/licenses/by ( (10) Consider the following generalized Caputo fractional differential equation [38]: (11) Subject to (12) The CF differential equation (11) has equilibrium point if and only if .…”

Section: Properties [36]mentioning

confidence: 99%

Stability Analysis of Fractional SIR Model Related to Delay in State and Control Variables

Khalaf

Flayyih²

2021

basjs

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The study of a nonlinear mathematical fractional SIR (Susceptible - Infected - Recovered) epidemiological model related to the delay in state and control variables in terms of time is the focus of this paper. The existence of a bounded solution for the fractional SIR epidemic model has been demonstrated, and it is unique. A new set of infection-free equilibrium points has been discovered, and their local stability has been investigated. In addition, using the next-generation matrix method, the basic reproductive number Ro was calculated

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“…Muhmmad et al [15] analysed the effects of magnetic fields between two parallel walls for the unsteady double phase nano-fluid flow and heat transfer using Differential Transform Method. Khudir [9] extended the Differential Transform Method to Fractional Differential Transform Method (FDTM) and solved an irrational order fractional differential equations. Kundu et al [10] appllied DTM and investigated the thermal analysis of exponential fins under sensible and latent heat transfer.…”

Section: Introductionmentioning

confidence: 99%

Analytical Investigation of MHD Jeffery–Hamel flow problem with heat transfer by differential transform method

Meher

Patel

2019

SN Appl. Sci.

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The aim of this research paper is to study and analyse the effects of Reynolds number, Hartmann number and thermal profile on velocity profiles of magneto hydro dynamics Jeffery-Hamel fluid flow between two non-parallel plates with angles 2θ and electromagnetic induction (E 0). An approximate analytical solution of the problem that is formulated using the Navier-Stokes and continuity equations has obtained in the form of a convergent series using differential transform method. The nature and the variation of the velocity profiles of Jeffery-Hamel flow with heat transfer are discussed herewith considering different thermal profiles with distinct positive values of Ha and Re in both convergent and divergent channels. The authenticity and the usefulness of this method have demonstrated by comparing with the available results of optimal homotopy perturbation method and the numerical method. Keywords Differential transform method • Heat transfer • Jeffery-Hamel flow • System of differential equations List of symbols P Pressure k Conductivity of the thermal ρ Density T Temperature Re Reynolds number E 0 Electromagnetic induction v Kinematic viscosity M Magnetic field θ Half-angle between the two plates Ha Hartmann number

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Restricted fractional differential transform for solving irrational order fractional differential equations

Cited by 24 publications

References 31 publications

Dropout Deep Belief Network Based Chinese Ancient Ceramic Non-Destructive Identification

Dropout Deep Belief Network Based Chinese Ancient Ceramic Non-Destructive Identification

Stability Analysis of Fractional SIR Model Related to Delay in State and Control Variables

Analytical Investigation of MHD Jeffery–Hamel flow problem with heat transfer by differential transform method

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