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15-02-2022 | Original Article

A new iterative technique for solving fractal-fractional differential equations based on artificial neural network in the new generalized Caputo sense

Authors: A. M. Shloof, N. Senu, A. Ahmadian, M. Pakdaman, S. Salahshour

Published in: Engineering with Computers | Issue 1/2023

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Abstract

This paper attempts to create an artificial neural networks (ANNs) technique for solving well-known fractal-fractional differential equations (FFDEs). FFDEs have the advantage of being able to help explain a variety of real-world physical problems. The technique implemented in this paper converts the original differential equation into a minimization problem using a suggested truncated power series of the solution function. Next, answer to the problem is obtained via computing the parameters with highly precise neural network model. We can get a good approximate solution of FFDEs by combining the initial conditions with the ANNs performance. Examples are provided to portray the efficiency and applicability of this method. Comparison with similar existing approaches are also conducted to demonstrate the accuracy of the proposed approach.

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Title: A new iterative technique for solving fractal-fractional differential equations based on artificial neural network in the new generalized Caputo sense
Authors: A. M. Shloof
N. Senu
A. Ahmadian
M. Pakdaman
S. Salahshour
Publication date: 15-02-2022
Publisher: Springer London
Published in: Engineering with Computers / Issue 1/2023
Print ISSN: 0177-0667
Electronic ISSN: 1435-5663
DOI: https://doi.org/10.1007/s00366-022-01607-8

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