### Abstract

In mathematical modeling of Artificial Neural Networks (ANN), a neuron's network function formulates as an arrangement of other functions. It represents a composition of other functions by using arrows between variables. In this paper, we introduce a new class of activation functions based on the concept of the univex function. This type of functions satisfies the convexity property. This property converges to the outcome of ANN. Moreover, we study the activation function by using the concept of approximation theory. Finally, we lay new connections of the nonlinear weighted sum depending on the fractional power. The simulation is introduced to maximize the utility function in a fractional cloud computing system.

Original language | English |
---|---|

Pages (from-to) | 285-299 |

Number of pages | 15 |

Journal | International Journal of Mathematics and Computer Science |

Volume | 14 |

Issue number | 1 |

Publication status | Published - 1 Jan 2019 |

### Fingerprint

### Keywords

- Activation function
- ANN
- Fractional calculus
- Fractional difference problem
- System operators

### ASJC Scopus subject areas

- Computer Science (miscellaneous)
- Algebra and Number Theory
- Statistics and Probability
- Numerical Analysis
- Modelling and Simulation
- Discrete Mathematics and Combinatorics
- Computational Mathematics
- Applied Mathematics

### Cite this

**Evaluation of proximity points for a class of neuron's network functions based on local fractional calculus.** / Ibrahim, Rabha W.; Darus, Maslina.

Research output: Contribution to journal › Article

*International Journal of Mathematics and Computer Science*, vol. 14, no. 1, pp. 285-299.

}

TY - JOUR

T1 - Evaluation of proximity points for a class of neuron's network functions based on local fractional calculus

AU - Ibrahim, Rabha W.

AU - Darus, Maslina

PY - 2019/1/1

Y1 - 2019/1/1

N2 - In mathematical modeling of Artificial Neural Networks (ANN), a neuron's network function formulates as an arrangement of other functions. It represents a composition of other functions by using arrows between variables. In this paper, we introduce a new class of activation functions based on the concept of the univex function. This type of functions satisfies the convexity property. This property converges to the outcome of ANN. Moreover, we study the activation function by using the concept of approximation theory. Finally, we lay new connections of the nonlinear weighted sum depending on the fractional power. The simulation is introduced to maximize the utility function in a fractional cloud computing system.

AB - In mathematical modeling of Artificial Neural Networks (ANN), a neuron's network function formulates as an arrangement of other functions. It represents a composition of other functions by using arrows between variables. In this paper, we introduce a new class of activation functions based on the concept of the univex function. This type of functions satisfies the convexity property. This property converges to the outcome of ANN. Moreover, we study the activation function by using the concept of approximation theory. Finally, we lay new connections of the nonlinear weighted sum depending on the fractional power. The simulation is introduced to maximize the utility function in a fractional cloud computing system.

KW - Activation function

KW - ANN

KW - Fractional calculus

KW - Fractional difference problem

KW - System operators

UR - http://www.scopus.com/inward/record.url?scp=85071180336&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85071180336&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85071180336

VL - 14

SP - 285

EP - 299

JO - International Journal of Mathematics and Computer Science

JF - International Journal of Mathematics and Computer Science

SN - 1814-0424

IS - 1

ER -