New Aspects of Bloch Model Associated with Fractal Fractional Derivatives

To model complex real world problems, the novel concept of non-local fractal-fractional differential and integral operators with two orders (fractional order and fractal dimension) have been used as mathematical tools in contrast to classical derivatives and integrals. In this paper, we consider Blo...

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Autores principales:	Akgül Ali, Mallah Ishfaq Ahmad, Alha Subhash
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/e9af57505a584bee95cdf00b0abaa426
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spelling	oai:doaj.org-article:e9af57505a584bee95cdf00b0abaa4262021-12-05T14:10:57ZNew Aspects of Bloch Model Associated with Fractal Fractional Derivatives2192-80102192-802910.1515/nleng-2021-0026https://doaj.org/article/e9af57505a584bee95cdf00b0abaa4262021-11-01T00:00:00Zhttps://doi.org/10.1515/nleng-2021-0026https://doaj.org/toc/2192-8010https://doaj.org/toc/2192-8029To model complex real world problems, the novel concept of non-local fractal-fractional differential and integral operators with two orders (fractional order and fractal dimension) have been used as mathematical tools in contrast to classical derivatives and integrals. In this paper, we consider Bloch equations with fractal-fractional derivatives. We find the general solutions for components of magnetization ℳ = (Mu, Mv, Mw) by using descritization and Lagrange's two step polynomial interpolation. We analyze the model with three different kernels namely power function, exponential decay function and Mittag-Leffler type function. We provide graphical behaviour of magnetization components ℳ = (Mu, Mv, Mw) on different orders. The examination of Bloch equations with fractal-fractional derivatives show new aspects of Bloch equations.Akgül AliMallah Ishfaq AhmadAlha SubhashDe GruyterarticleEngineering (General). Civil engineering (General)TA1-2040ENNonlinear Engineering, Vol 10, Iss 1, Pp 323-342 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Engineering (General). Civil engineering (General) TA1-2040
spellingShingle	Engineering (General). Civil engineering (General) TA1-2040 Akgül Ali Mallah Ishfaq Ahmad Alha Subhash New Aspects of Bloch Model Associated with Fractal Fractional Derivatives
description	To model complex real world problems, the novel concept of non-local fractal-fractional differential and integral operators with two orders (fractional order and fractal dimension) have been used as mathematical tools in contrast to classical derivatives and integrals. In this paper, we consider Bloch equations with fractal-fractional derivatives. We find the general solutions for components of magnetization ℳ = (Mu, Mv, Mw) by using descritization and Lagrange's two step polynomial interpolation. We analyze the model with three different kernels namely power function, exponential decay function and Mittag-Leffler type function. We provide graphical behaviour of magnetization components ℳ = (Mu, Mv, Mw) on different orders. The examination of Bloch equations with fractal-fractional derivatives show new aspects of Bloch equations.
format	article
author	Akgül Ali Mallah Ishfaq Ahmad Alha Subhash
author_facet	Akgül Ali Mallah Ishfaq Ahmad Alha Subhash
author_sort	Akgül Ali
title	New Aspects of Bloch Model Associated with Fractal Fractional Derivatives
title_short	New Aspects of Bloch Model Associated with Fractal Fractional Derivatives
title_full	New Aspects of Bloch Model Associated with Fractal Fractional Derivatives
title_fullStr	New Aspects of Bloch Model Associated with Fractal Fractional Derivatives
title_full_unstemmed	New Aspects of Bloch Model Associated with Fractal Fractional Derivatives
title_sort	new aspects of bloch model associated with fractal fractional derivatives
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/e9af57505a584bee95cdf00b0abaa426
work_keys_str_mv	AT akgulali newaspectsofblochmodelassociatedwithfractalfractionalderivatives AT mallahishfaqahmad newaspectsofblochmodelassociatedwithfractalfractionalderivatives AT alhasubhash newaspectsofblochmodelassociatedwithfractalfractionalderivatives
_version_	1718371575650058240

New Aspects of Bloch Model Associated with Fractal Fractional Derivatives

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