An optimal neural network design for fractional deep learning of logistic growth

Wei, Jia-Li; Wu, Guo–Cheng; Liu, Bao-Qing; Nieto, Juan J.

doi:10.1007/s00521-023-08268-8

Cited by 10 publications

(1 citation statement)

References 27 publications

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“…The logistic differential equation has many applications in different fields. Recently, the fractional version of the logistic equation has been considered by several authors [5,6,[9][10][11][12][13]. Power series representation of the solution of the fractional logistic equation and the existence of solution is discussed in Area and Nieto [10].…”

Section: Introductionmentioning

confidence: 99%

Hybrid Fibonacci wavelet method to solve fractional‐order logistic growth model

Ahmed

Jahan

Nisar

2023

Math Methods in App Sciences

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The aim of this study is to develop the Fibonacci wavelet method together with the quasi‐linearization technique to solve the fractional‐order logistic growth model. The block‐pulse functions are employed to construct the operational matrices of fractional‐order integration. The fractional derivative is described in the Caputo sense. The present time‐fractional population growth model is converted into a set of nonlinear algebraic equations using the proposed generated matrices. Making use of the quasi‐linearization technique, the underlying equations are then changed to a set of linear equations. Numerical simulations are conducted to show the reliability and use of the suggested approach when contrasted with methods from the existing literature. A comparison of several numerical techniques from the available literature is presented to show the efficacy and correctness of the suggested approach.

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Section: Introductionmentioning

confidence: 99%

Hybrid Fibonacci wavelet method to solve fractional‐order logistic growth model

Ahmed

Jahan

Nisar

2023

Math Methods in App Sciences

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A new lower bound for the $$\textrm{L}^2$$-norm of the Caputo fractional derivative

Jornet

2024

Arch. Math.

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We prove a novel, tight lower bound for the norm in $$\textrm{L}^2[0,T]$$ L 2 [ 0 , T ] of the Caputo fractional derivative. It is based on continuous linear functionals, Peano kernels, and the Gaussian hypergeometric function.

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A hybrid technique based on Lucas polynomials for solving fractional diffusion partial differential equation

Kawala,

Abdelaziz

2023

J Elliptic Parabol Equ

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This paper presents a new numerical technique to approximate solutions of diffusion partial differential equations with Caputo fractional derivatives. We use a spectral collocation method based on Lucas polynomials for time fractional derivatives and a finite difference scheme in space. Stability and error analyses of the proposed technique are established. To demonstrate the reliability and efficiency of our new technique, we applied the method to a number of examples. The new technique is simply applicable, and the results show high efficiency in calculation and approximation precision.

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An optimal neural network design for fractional deep learning of logistic growth

Cited by 10 publications

References 27 publications

Hybrid Fibonacci wavelet method to solve fractional‐order logistic growth model

Hybrid Fibonacci wavelet method to solve fractional‐order logistic growth model

A new lower bound for the $$\textrm{L}^2$$-norm of the Caputo fractional derivative

A hybrid technique based on Lucas polynomials for solving fractional diffusion partial differential equation

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