j. inst. sci. and tech. Journal of the Institute of Science and Technology 2536-4618 Igdir University 10.21597/jist.1230287 Mathematical Sciences Matematik Investigation of Solutions of 𝜷 −conformable Fractional Ordinary Differential Equation With Artificial Neural Network https://orcid.org/0000-0001-5026-6534 Bulut Sadullah ERZURUM TECHNICAL UNIVERSITY https://orcid.org/0000-0003-4255-5760 Yiğider Muhammed ERZURUM TECHNICAL UNIVERSITY 06 01 2023 13 2 1266 1274 01 06 2023 02 23 2023 Copyright © 2011, Journal of the Institute of Science and Technology 2011 Journal of the Institute of Science and Technology

Ä°n this study, we present a method in order to get initial value fractional differential equations with artificial neural networks. On the basis of the function approach of feedforward neural networks, this method is a general method that is written in an implicit analytical form and results in the creation of a differentiable solution. The first part of the created trial solution which is stated as the sum of the two parts, with no controllable parameters, gives the initial conditions. The second part, unaffected by the initial conditions, consists of a feedforward neural network with controllable parameters (weights). The applicability of this approach is demonstrated in systems of both fractional single ODEs and fractional coupled ODEs.

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