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

Kumar P., Ertürk V. S., Murillo-Arcila M., Govindaraj V.

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, vol.31, no.4, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 31 Issue: 4
  • Publication Date: 2023
  • Doi Number: 10.1142/s0218348x23400431
  • Journal Name: FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Compendex, INSPEC, zbMATH, DIALNET, Civil Engineering Abstracts
  • Keywords: Neural Networks, Delay-Type Mathematical Model, Caputo Fractional Derivative, L1-Predictor-Corrector Method, Graphical Simulations, DIFFERENTIAL EQUATIONS
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

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.