$Numerical solution of variable-order time fractional weakly singular partial integro-differential equations with error estimation$

Numerical solution of variable-order time fractional weakly singular partial integro-differential equations with error estimation

In this paper, we apply Legendre-Laguerre functions (LLFs) and collocation method to obtain the approximate solution of variable-order time-fractional partial integro-diﬀerential equations (VO-TF-PIDEs) with the weakly singular kernel. For this purpose, we derive the pseudo-operational matrices wit...

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Main Authors:	Haniye Dehestani, Yadollah Ordokhani, Mohsen Razzaghi
Format:	Article
Language:	English
Published:	Vilnius Gediminas Technical University 2020-10-01
Series:	Mathematical Modelling and Analysis
Subjects:	variable-order fractional partial integro-diﬀerential equations weakly singular kernel Legendre-Laguerre functions pseudo-operational matrix
Online Access:	https://www.bjrbe.vgtu.lt/index.php/MMA/article/view/11692

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spelling	doaj-43c829a9038c4d36a56503d2ee02f8d82021-07-02T14:50:14ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102020-10-0125410.3846/mma.2020.11692Numerical solution of variable-order time fractional weakly singular partial integro-differential equations with error estimationHaniye Dehestani0Yadollah Ordokhani1Mohsen Razzaghi2Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, IranDepartment of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, IranDepartment of Mathematics and Statistics, Mississippi State University, Starkville, 39762 MS, USA In this paper, we apply Legendre-Laguerre functions (LLFs) and collocation method to obtain the approximate solution of variable-order time-fractional partial integro-diﬀerential equations (VO-TF-PIDEs) with the weakly singular kernel. For this purpose, we derive the pseudo-operational matrices with the use of the transformation matrix. The collocation method and pseudo-operational matrices transfer the problem to a system of algebraic equations. Also, the error analysis of the proposed method is given. We consider several examples to illustrate the proposed method is accurate. https://www.bjrbe.vgtu.lt/index.php/MMA/article/view/11692variable-order fractional partial integro-diﬀerential equationsweakly singular kernelLegendre-Laguerre functionspseudo-operational matrix
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Haniye Dehestani Yadollah Ordokhani Mohsen Razzaghi
spellingShingle	Haniye Dehestani Yadollah Ordokhani Mohsen Razzaghi Numerical solution of variable-order time fractional weakly singular partial integro-differential equations with error estimation Mathematical Modelling and Analysis variable-order fractional partial integro-diﬀerential equations weakly singular kernel Legendre-Laguerre functions pseudo-operational matrix
author_facet	Haniye Dehestani Yadollah Ordokhani Mohsen Razzaghi
author_sort	Haniye Dehestani
title	Numerical solution of variable-order time fractional weakly singular partial integro-differential equations with error estimation
title_short	Numerical solution of variable-order time fractional weakly singular partial integro-differential equations with error estimation
title_full	Numerical solution of variable-order time fractional weakly singular partial integro-differential equations with error estimation
title_fullStr	Numerical solution of variable-order time fractional weakly singular partial integro-differential equations with error estimation
title_full_unstemmed	Numerical solution of variable-order time fractional weakly singular partial integro-differential equations with error estimation
title_sort	numerical solution of variable-order time fractional weakly singular partial integro-differential equations with error estimation
publisher	Vilnius Gediminas Technical University
series	Mathematical Modelling and Analysis
issn	1392-6292 1648-3510
publishDate	2020-10-01
description	In this paper, we apply Legendre-Laguerre functions (LLFs) and collocation method to obtain the approximate solution of variable-order time-fractional partial integro-diﬀerential equations (VO-TF-PIDEs) with the weakly singular kernel. For this purpose, we derive the pseudo-operational matrices with the use of the transformation matrix. The collocation method and pseudo-operational matrices transfer the problem to a system of algebraic equations. Also, the error analysis of the proposed method is given. We consider several examples to illustrate the proposed method is accurate.
topic	variable-order fractional partial integro-diﬀerential equations weakly singular kernel Legendre-Laguerre functions pseudo-operational matrix
url	https://www.bjrbe.vgtu.lt/index.php/MMA/article/view/11692
work_keys_str_mv	AT haniyedehestani numericalsolutionofvariableordertimefractionalweaklysingularpartialintegrodifferentialequationswitherrorestimation AT yadollahordokhani numericalsolutionofvariableordertimefractionalweaklysingularpartialintegrodifferentialequationswitherrorestimation AT mohsenrazzaghi numericalsolutionofvariableordertimefractionalweaklysingularpartialintegrodifferentialequationswitherrorestimation
_version_	1721327685685215232

Numerical solution of variable-order time fractional weakly singular partial integro-differential equations with error estimation

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