A NEW FORM OF L1-PREDICTOR-CORRECTOR SCHEME TO SOLVE MULTIPLE DELAY-TYPE FRACTIONAL ORDER SYSTEMS WITH THE EXAMPLE OF A NEURAL NETWORK MODEL

被引：12

作者：

Kumar, Pushpendra ^{[1
]}

Erturk, Vedat Suat ^{[2
]}

Murillo-Arcila, Marina ^{[3
]}

Govindaraj, V. ^{[1
]}

机构：

[1] Natl Inst Technol Puducherry, Dept Math, Karaikal 609609, India

[2] Ondokuz Mayis Univ, Fac Arts & Sci, Dept Math, TR-55200 Samsun, Turkiye

[3] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Valencia 46022, Spain

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2023年 / 31卷 / 04期

关键词：

Neural Networks; Delay-Type Mathematical Model; Caputo Fractional Derivative; L1-Predictor-Corrector Method; Graphical Simulations; DIFFERENTIAL EQUATIONS;

D O I：

10.1142/S0218348X23400431

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we derive a new version of L1-Predictor-Corrector (L1-PC) method by using some previously given methods (L1-PC for single delay, PC for non-delay, and decomposition algorithm) to solve multiple delay-type fractional differential equations. The Caputo fractional derivative with singular type kernel is used to establish the results. Some important remarks related to the delay term estimation and error analysis are mentioned. In order to check the accuracy and correctness of our method, we solve a neural network system with two delay parameters. A number of graphs are given to justify the role of delays as well as the accuracy of the algorithm. The given method is fully novel and reliable to solve multiple delay type fractional order systems in Caputo sense.

引用

页数：13

共 36 条

[1] A mathematical study of a tuberculosis model with fractional derivatives [J].