Picard Method for Existence, Uniqueness, and Gauss Hypergeomatric Stability of the Fractional-Order Differential Equations

Picard Method for Existence, Uniqueness, and Gauss Hypergeomatric Stability of the Fractional-Order Differential Equations

In this paper, we consider a class of fractional-order differential equations and investigate two aspects of these equations. First, we consider the existence of a unique solution, and then, using a new class of control functions, we investigate the Gauss hypergeometric stability. We use Chebyshev a...

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Main Authors: Zahra Eidinejad, Reza Saadati, Manuel De La Sen
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2021/7074694
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spelling doaj-bf70fd98aea946c99145245de6dcd5532021-08-02T00:00:14ZengHindawi LimitedMathematical Problems in Engineering1563-51472021-01-01202110.1155/2021/7074694Picard Method for Existence, Uniqueness, and Gauss Hypergeomatric Stability of the Fractional-Order Differential EquationsZahra Eidinejad0Reza Saadati1Manuel De La Sen2School of MathematicsSchool of MathematicsInstitute of Research and Development of Processes IIDPIn this paper, we consider a class of fractional-order differential equations and investigate two aspects of these equations. First, we consider the existence of a unique solution, and then, using a new class of control functions, we investigate the Gauss hypergeometric stability. We use Chebyshev and Bielecki norms in order to prove these aspects by the Picard method. Finally, we give some examples to illustrate our results.http://dx.doi.org/10.1155/2021/7074694
collection DOAJ
language English
format Article
sources DOAJ
author Zahra Eidinejad
Reza Saadati
Manuel De La Sen
spellingShingle Zahra Eidinejad
Reza Saadati
Manuel De La Sen
Picard Method for Existence, Uniqueness, and Gauss Hypergeomatric Stability of the Fractional-Order Differential Equations
Mathematical Problems in Engineering
author_facet Zahra Eidinejad
Reza Saadati
Manuel De La Sen
author_sort Zahra Eidinejad
title Picard Method for Existence, Uniqueness, and Gauss Hypergeomatric Stability of the Fractional-Order Differential Equations
title_short Picard Method for Existence, Uniqueness, and Gauss Hypergeomatric Stability of the Fractional-Order Differential Equations
title_full Picard Method for Existence, Uniqueness, and Gauss Hypergeomatric Stability of the Fractional-Order Differential Equations
title_fullStr Picard Method for Existence, Uniqueness, and Gauss Hypergeomatric Stability of the Fractional-Order Differential Equations
title_full_unstemmed Picard Method for Existence, Uniqueness, and Gauss Hypergeomatric Stability of the Fractional-Order Differential Equations
title_sort picard method for existence, uniqueness, and gauss hypergeomatric stability of the fractional-order differential equations
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1563-5147
publishDate 2021-01-01
description In this paper, we consider a class of fractional-order differential equations and investigate two aspects of these equations. First, we consider the existence of a unique solution, and then, using a new class of control functions, we investigate the Gauss hypergeometric stability. We use Chebyshev and Bielecki norms in order to prove these aspects by the Picard method. Finally, we give some examples to illustrate our results.
url http://dx.doi.org/10.1155/2021/7074694
work_keys_str_mv AT zahraeidinejad picardmethodforexistenceuniquenessandgausshypergeomatricstabilityofthefractionalorderdifferentialequations
AT rezasaadati picardmethodforexistenceuniquenessandgausshypergeomatricstabilityofthefractionalorderdifferentialequations
AT manueldelasen picardmethodforexistenceuniquenessandgausshypergeomatricstabilityofthefractionalorderdifferentialequations
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