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, cilt.31, sa.4, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 31 Sayı: 4
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1142/s0218348x23400431
  • Dergi Adı: FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Compendex, INSPEC, zbMATH, DIALNET, Civil Engineering Abstracts
  • Anahtar Kelimeler: Neural Networks, Delay-Type Mathematical Model, Caputo Fractional Derivative, L1-Predictor-Corrector Method, Graphical Simulations, DIFFERENTIAL EQUATIONS
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

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.