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Solving fractal differential equations via fractal Laplace transforms

Solving fractal differential equations via fractal Laplace transforms AbstractThe intention of this study is to investigate the fractal version of both one-term and three-term fractal differential equations. The fractal Laplace transform of the local derivative and the non-local fractal Caputo derivative is applied to investigate the given models. The analogues of both the Wright function with its related definitions in fractal calculus and the convolution theorem in fractal calculus are proposed. All results in this paper have been obtained by applying certain tools such as the general Wright and Mittag-Leffler functions of three parameters and the convolution theorem in the sense of the fractal calculus. Moreover, a comparative analysis is conducted by solving the governing equation in the senses of the standard version and fractal calculus.It is obvious that when α=γ=β=1{\alpha=\gamma=\beta=1}, we obtain the same results as in the standard version. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Analysis de Gruyter

Solving fractal differential equations via fractal Laplace transforms

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Publisher
de Gruyter
Copyright
© 2022 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1869-6082
eISSN
1869-6082
DOI
10.1515/jaa-2021-2076
Publisher site
See Article on Publisher Site

Abstract

AbstractThe intention of this study is to investigate the fractal version of both one-term and three-term fractal differential equations. The fractal Laplace transform of the local derivative and the non-local fractal Caputo derivative is applied to investigate the given models. The analogues of both the Wright function with its related definitions in fractal calculus and the convolution theorem in fractal calculus are proposed. All results in this paper have been obtained by applying certain tools such as the general Wright and Mittag-Leffler functions of three parameters and the convolution theorem in the sense of the fractal calculus. Moreover, a comparative analysis is conducted by solving the governing equation in the senses of the standard version and fractal calculus.It is obvious that when α=γ=β=1{\alpha=\gamma=\beta=1}, we obtain the same results as in the standard version.

Journal

Journal of Applied Analysis – de Gruyter

Published: Dec 1, 2022

Keywords: Fractal calculus; fractal Wright function; fractal Laplace transform; fractal convolution theorem; 28A80; 81Q35; 44A10

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