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

Pushpendra Kumar, Vedat Suat Erturk, Marina Murillo-Arcila and V. Govindaraj
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Pushpendra Kumar: Department of Mathematics, National Institute of Technology Puducherry, Karaikal 609609, India
Vedat Suat Erturk: ��Department of Mathematics, Faculty of Arts and Sciences, Ondokuz Mayis University, Atakum 55200, Samsun, Turkey
Marina Murillo-Arcila: ��Instituto Universitario de Matematica Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain
V. Govindaraj: Department of Mathematics, National Institute of Technology Puducherry, Karaikal 609609, India

FRACTALS (fractals), 2023, vol. 31, issue 04, 1-13

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.

Keywords: Neural Networks; Delay-Type Mathematical Model; Caputo Fractional Derivative; L1-Predictor–Corrector Method; Graphical Simulations (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23400431

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