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A stochastic neural network process for the fractional order lungs cancer operation system Cover

A stochastic neural network process for the fractional order lungs cancer operation system

Open Access
|Mar 2026

Figures & Tables

Fig. 1

Neural network values using LMBP for the FLCOS.

Fig. 2

A single process of neural network for the FLCOS.

Fig. 3

A design of neural network with the training of LMBP for the FLCOS.

Fig. 4

Optimal training values and Trans. State for the FLCOS.

Fig. 5

Optimal training values and Trans. State for the FLCOS.

Fig. 6

Regression values for case (1) of FLCOS.

Fig. 7

Regression values for case (2) of FLCOS.

Fig. 8

Regression values for case (3) of FLCOS.

Fig. 9

Output values for the FLCOS using the training of LMBP.

Fig. 10

Output values for the FLCOS using the training of LMBP.

Angular deceleration vs time_

ParametersDefinition
λCell rate of developing cancer
gCompetence of transport
β1Immune cells effects
β3Transporting cancer cell nutrients and sanctioning metastasis
ϕ1, ϕ2, ϕ3Growth factor effects
θTime
β2Association in immunity cells and cancer growing
δRemaining parts of the body and spreading of death rate of cancer cells
μSpreading rate of the cells of cancer via lungs tissue using the outstanding body organs
γRate of cancer cells based tissue expanding in lungs to remaining parts of bod
k1, k2, k3Initial conditions (ICs)

Training procedure for the FLCOS using the LMBP_

CaseMSE(Train)MSE(Validation)MSE(Testing)PerformanceGradientMuIterationComplexity
13.10307x10−112.81833x10−116.62677x10−113.10x10−114.81x10−091.00x10−12311 sec
25.70217x10−098.91222x10−097.17650x10−095.70x10−097.23x10−081.00x10−11141 sec
35.54041x10−098.50954x10−098.88814x10−095.54x10−092.98x10−081.00x10−10071 sec
Language: English
Submitted on: Jun 25, 2025
Accepted on: Jan 1, 2026
Published on: Mar 18, 2026
Published by: Harran University
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2026 Gilder Cieza Altamirano, published by Harran University
This work is licensed under the Creative Commons Attribution 4.0 License.

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