A new efficient algorithm based on feedforward neural network for solving differential equations of fractional order

Admon, Mohd Rashid; Senu, Norazak; Ahmadian, Ali; Majid, Zanariah Abdul; Salahshour, Soheil

doi:10.1016/j.cnsns.2022.106968

Cited by 15 publications

(4 citation statements)

References 42 publications

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“…We train FNN [ 73 , 74 ] and RNN [ 75 ] with a sequential model that allows for layer-by-layer training [ 76 ]. The activation functions are an integral part of neural networks.…”

Section: Resultsmentioning

confidence: 99%

A machine learning and deep learning-based integrated multi-omics technique for leukemia prediction

Abbasi,

Deng,

Ali

et al. 2024

Heliyon

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“…We train FNN [ 73 , 74 ] and RNN [ 75 ] with a sequential model that allows for layer-by-layer training [ 76 ]. The activation functions are an integral part of neural networks.…”

Section: Resultsmentioning

confidence: 99%

A machine learning and deep learning-based integrated multi-omics technique for leukemia prediction

Abbasi,

Deng,

Ali

et al. 2024

Heliyon

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“…the method of solving equation ( 14) presented in the appendix, it can be derived that equation ( 14) always has unique positive roots for q 2 3 , 1 . Î ⎛ ⎝ ⎞ ⎠ Next, by substituting the above positive real roots into equation (13), the Hopf bifurcation threshold e 2 * can be obtained. The evolution trend of e 2 * with the differential order q is exhibited in figure 6.…”

Section: = -mentioning

confidence: 99%

“…However, the exact solutions of FDEs are difficult to obtain, so developing high-precision numerical methods to solve FDEs has become an important research field. In recent years, various numerical methods have been proposed, such as wavelet methods [9], finite difference methods [10], operator matrix solution methods [11], predictor-corrector methods [12], and neural network-based methods [13]. Meanwhile, many works have paid attention to the stability analysis of complex FDEs, such as high-order fractional delay differential equations [14], fractional neutral functional stochastic differential equations with infinite delay [15], and fractional fuzzy stochastic differential equations with delay [16].…”

Section: Introductionmentioning

confidence: 99%

A novel entanglement functions-based 4D fractional-order chaotic system and its bifurcation analysis

Tang,

Li,

Huang

2024

Phys. Scr.

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A novel 4D fractional-order chaotic entanglement system based on sinusoidal functions is established in this paper. We aim to reveal the relationship between the dynamical behavior of the new system and its entanglement coefficients. It is found that the equilibrium point of the system varies regularly with the successive change of the entanglement coefficient. The supercritical pitchfork bifurcation phenomenon of the new system is discussed based on the fractional-order stability theory. Furthermore, sufficient conditions and threshold for supercritical Hopf bifurcation caused by the entanglement coefficient are provided. Finally, the route to chaos of the new system is explored utilizing multiple numerical indicators, such as spectral entropy complexity, bifurcation diagrams, Lyapunov exponential spectrum, phase portraits, and 0-1 test curves. The results indicate that in addition to various chaotic attractors, there are phenomena such as period-doubling bifurcations, period windows, and coexisting symmetric attractors (periodic or chaotic).

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“…Reference source not found.). These layers typically include an input layer, one or more hidden layers, and an output layer [37]. Each neuron in a layer is connected to every neuron in the subsequent layer, but there are no connections that loop back within the same layer or to previous layers.…”

Section: Feedforward Neural Networkmentioning

confidence: 99%

Multiple Sclerosis Recognition via Wavelet Entropy and PSO-Based Neural Network

Lima

2023

Preprint

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This paper presents a novel approach for the recognition of multiple sclerosis (MS) using wavelet entropy and a Particle Swarm Optimization (PSO)-based neural network. MS is a complex neurological disorder with diverse clinical manifestations, often challenging to diagnose accurately. In this study, we leverage wavelet entropy (WE) as a feature extraction method to capture intricate patterns within brain imaging data. These extracted features are then employed to train a neural network model optimized through PSO to enhance classification accuracy. Experimental results on a dataset comprising MS and healthy control subjects demonstrate the effectiveness of our proposed approach, viz., WE-PSONN, which achieves a sensitivity of 91.95±1.15, a specificity of 92.36±0.88, a precision of 92.28±0.88, an accuracy of 92.16±0.90. The combination of advanced signal processing techniques and machine learning optimization holds promise for improving the early diagnosis and management of MS, offering potential benefits to both patients and healthcare providers.

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A new efficient algorithm based on feedforward neural network for solving differential equations of fractional order

Cited by 15 publications

References 42 publications

A machine learning and deep learning-based integrated multi-omics technique for leukemia prediction

A machine learning and deep learning-based integrated multi-omics technique for leukemia prediction

A novel entanglement functions-based 4D fractional-order chaotic system and its bifurcation analysis

Multiple Sclerosis Recognition via Wavelet Entropy and PSO-Based Neural Network

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