Artificial neural network for solving the nonlinear singular fractional differential equations

被引：7

作者：

Althubiti, Saeed ^{[1
]}

Kumar, Manoj ^{[2
]}

Goswami, Pranay ^{[2
]}

Kumar, Kranti ^{[2
,3
]}

机构：

[1] Taif Univ, Coll Sci, Dept Math, Taif, Saudi Arabia

[2] Dr BR Ambedkar Univeristy Delhi, Sch Liberal Studies, Delhi 110006, India

[3] Cent Univ Himachal Pradesh, Dept Math, Dharamshala, Himachal Prades, India

来源：

APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING | 2023年 / 31卷 / 01期

关键词：

MLP neural network; nonlinear fractional differential equation; unsupervised learning; approximate solutions;

D O I：

10.1080/27690911.2023.2187389

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

This paper proposes an artificial neural network (ANN) architecture for solving nonlinear fractional differential equations. The proposed ANN algorithm is based on a truncated power series expansion to substitute the unknown functions in the equations in this approach. Then, a set of algebraic equations is resolved using the ANN technique in an iterative minimization process. Finally, numerical examples are provided to demonstrate the usefulness of the ANN architectures. The results verify that the suggested ANN architecture achieves high accuracy and good stability.

引用

页数：17

共 50 条

[41] The two variable (φ′/φ, 1/φ)-expansion method for solving the time-fractional partial differential equations
Zhao, Yunmei
He, Yinghui
Yang, Huizhang
[J]. AIMS MATHEMATICS, 2020, 5 (05): : 4121 - 4135
[42] Iterative Algorithm for Solving Scalar Fractional Differential Equations with Riemann-Liouville Derivative and Supremum
Agarwal, Ravi
Hristova, Snezhana
O'Regan, Donal
Stefanova, Kremena
[J]. ALGORITHMS, 2020, 13 (08)
[43] NUMERICAL SCHEME METHODS FOR SOLVING NONLINEAR PSEUDO-HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS
Abdulazeez, Sadeq Taha
Modanli, Mahmut
Husien, Ahmad Muhamad
[J]. JOURNAL OF APPLIED MATHEMATICS AND COMPUTATIONAL MECHANICS, 2022, 21 (04) : 5 - 15
[44] Solving a Nonlinear Fractional Differential Equation Using Fixed Point Results in Orthogonal Metric Spaces
Abdou, Afrah Ahmad Noman
[J]. FRACTAL AND FRACTIONAL, 2023, 7 (11)
[45] A simple technique for constructing exact solutions to nonlinear differential equations with conformable fractional derivative
Melike Kaplan
Ahmet Bekir
Mehmet Naci Ozer
[J]. Optical and Quantum Electronics, 2017, 49
[46] Solitary wave solutions for some nonlinear time-fractional partial differential equations
S Z Hassan
Mahmoud A E Abdelrahman
[J]. Pramana, 2018, 91
[47] Solitary wave solutions for some nonlinear time-fractional partial differential equations
Hassan, S. Z.
Abdelrahman, Mahmoud A. E.
[J]. PRAMANA-JOURNAL OF PHYSICS, 2018, 91 (05):
[48] Finite difference methods with non-uniform meshes for nonlinear fractional differential equations
Li, Changpin
Yi, Qian
Chen, An
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 316 : 614 - 631
[49] Analytical and numerical solutions of multi-term nonlinear fractional orders differential equations
El-Sayed, A. M. A.
El-Kalla, I. L.
Ziada, E. A. A.
[J]. APPLIED NUMERICAL MATHEMATICS, 2010, 60 (08) : 788 - 797
[50] A simple technique for constructing exact solutions to nonlinear differential equations with conformable fractional derivative
Kaplan, Melike
Bekir, Ahmet
Ozer, Mehmet Naci
[J]. OPTICAL AND QUANTUM ELECTRONICS, 2017, 49 (08)

← 1 2 3 4 5 →