Aboodh Transform Iterative Method for Solving Fractional Partial Differential Equation with Mittag–Leffler Kernel

The major aim of this paper is the presentation of Aboodh transform of the Atangana–Baleanu fractional differential operator both in Caputo and Riemann–Liouville sense by using the connection between the Laplace transform and the Aboodh transform. Moreover, we aim to obtain the approximate series so...

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Autores principales:	Michael A. Awuya, Dervis Subasi
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	integral transform Atangana–Baleanu fractional derivative fractional calculus Aboodh transform iterative method Mittag–Leffler function Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/0b0a7050bc0b4363b3aa46905a4fac62
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id	oai:doaj.org-article:0b0a7050bc0b4363b3aa46905a4fac62
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spelling	oai:doaj.org-article:0b0a7050bc0b4363b3aa46905a4fac622021-11-25T19:06:24ZAboodh Transform Iterative Method for Solving Fractional Partial Differential Equation with Mittag–Leffler Kernel10.3390/sym131120552073-8994https://doaj.org/article/0b0a7050bc0b4363b3aa46905a4fac622021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2055https://doaj.org/toc/2073-8994The major aim of this paper is the presentation of Aboodh transform of the Atangana–Baleanu fractional differential operator both in Caputo and Riemann–Liouville sense by using the connection between the Laplace transform and the Aboodh transform. Moreover, we aim to obtain the approximate series solutions for the time-fractional differential equations with an Atangana–Baleanu fractional differential operator in the Caputo sense using the Aboodh transform iterative method, which is the modification of the Aboodh transform by combining it with the new iterative method. The relation between the Laplace transform and the Aboodh transform is symmetrical. Some graphical illustrations are presented to describe the effect of the fractional order. The outcome reveals that Aboodh transform iterative method is easy to implement and adequately captures the behavior and the fractional effect of the fractional differential equation.Michael A. AwuyaDervis SubasiMDPI AGarticleintegral transformAtangana–Baleanu fractional derivativefractional calculusAboodh transform iterative methodMittag–Leffler functionMathematicsQA1-939ENSymmetry, Vol 13, Iss 2055, p 2055 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	integral transform Atangana–Baleanu fractional derivative fractional calculus Aboodh transform iterative method Mittag–Leffler function Mathematics QA1-939
spellingShingle	integral transform Atangana–Baleanu fractional derivative fractional calculus Aboodh transform iterative method Mittag–Leffler function Mathematics QA1-939 Michael A. Awuya Dervis Subasi Aboodh Transform Iterative Method for Solving Fractional Partial Differential Equation with Mittag–Leffler Kernel
description	The major aim of this paper is the presentation of Aboodh transform of the Atangana–Baleanu fractional differential operator both in Caputo and Riemann–Liouville sense by using the connection between the Laplace transform and the Aboodh transform. Moreover, we aim to obtain the approximate series solutions for the time-fractional differential equations with an Atangana–Baleanu fractional differential operator in the Caputo sense using the Aboodh transform iterative method, which is the modification of the Aboodh transform by combining it with the new iterative method. The relation between the Laplace transform and the Aboodh transform is symmetrical. Some graphical illustrations are presented to describe the effect of the fractional order. The outcome reveals that Aboodh transform iterative method is easy to implement and adequately captures the behavior and the fractional effect of the fractional differential equation.
format	article
author	Michael A. Awuya Dervis Subasi
author_facet	Michael A. Awuya Dervis Subasi
author_sort	Michael A. Awuya
title	Aboodh Transform Iterative Method for Solving Fractional Partial Differential Equation with Mittag–Leffler Kernel
title_short	Aboodh Transform Iterative Method for Solving Fractional Partial Differential Equation with Mittag–Leffler Kernel
title_full	Aboodh Transform Iterative Method for Solving Fractional Partial Differential Equation with Mittag–Leffler Kernel
title_fullStr	Aboodh Transform Iterative Method for Solving Fractional Partial Differential Equation with Mittag–Leffler Kernel
title_full_unstemmed	Aboodh Transform Iterative Method for Solving Fractional Partial Differential Equation with Mittag–Leffler Kernel
title_sort	aboodh transform iterative method for solving fractional partial differential equation with mittag–leffler kernel
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/0b0a7050bc0b4363b3aa46905a4fac62
work_keys_str_mv	AT michaelaawuya aboodhtransformiterativemethodforsolvingfractionalpartialdifferentialequationwithmittaglefflerkernel AT dervissubasi aboodhtransformiterativemethodforsolvingfractionalpartialdifferentialequationwithmittaglefflerkernel
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Aboodh Transform Iterative Method for Solving Fractional Partial Differential Equation with Mittag–Leffler Kernel

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