On Local Generalized Ulam–Hyers Stability for Nonlinear Fractional Functional Differential Equation

On Local Generalized Ulam–Hyers Stability for Nonlinear Fractional Functional Differential Equation

We discuss the existence of positive solution for a class of nonlinear fractional differential equations with delay involving Caputo derivative. Well-known Leray–Schauder theorem, Arzela–Ascoli theorem, and Banach contraction principle are used for the fixed point property and existence of a solutio...

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Main Authors: Dongming Nie, Azmat Ullah Khan Niazi, Bilal Ahmed
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2020/3276873
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spelling doaj-0f68aa1a4f9148258a75d5c76363779d2020-11-25T03:56:26ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472020-01-01202010.1155/2020/32768733276873On Local Generalized Ulam–Hyers Stability for Nonlinear Fractional Functional Differential EquationDongming Nie0Azmat Ullah Khan Niazi1Bilal Ahmed2Department of Common Courses, Anhui Xinhua University, Hefei 230088, ChinaDepartment of Mathematics, Xiangtan University, Xiangtan, Hunan 411105, ChinaDepartment of Mathematics and Statistics, University of Lahore, Sargodha, Lahore, PakistanWe discuss the existence of positive solution for a class of nonlinear fractional differential equations with delay involving Caputo derivative. Well-known Leray–Schauder theorem, Arzela–Ascoli theorem, and Banach contraction principle are used for the fixed point property and existence of a solution. We establish local generalized Ulam–Hyers stability and local generalized Ulam–Hyers–Rassias stability for the same class of nonlinear fractional neutral differential equations. The simulation of an example is also given to show the applicability of our results.http://dx.doi.org/10.1155/2020/3276873
collection DOAJ
language English
format Article
sources DOAJ
author Dongming Nie
Azmat Ullah Khan Niazi
Bilal Ahmed
spellingShingle Dongming Nie
Azmat Ullah Khan Niazi
Bilal Ahmed
On Local Generalized Ulam–Hyers Stability for Nonlinear Fractional Functional Differential Equation
Mathematical Problems in Engineering
author_facet Dongming Nie
Azmat Ullah Khan Niazi
Bilal Ahmed
author_sort Dongming Nie
title On Local Generalized Ulam–Hyers Stability for Nonlinear Fractional Functional Differential Equation
title_short On Local Generalized Ulam–Hyers Stability for Nonlinear Fractional Functional Differential Equation
title_full On Local Generalized Ulam–Hyers Stability for Nonlinear Fractional Functional Differential Equation
title_fullStr On Local Generalized Ulam–Hyers Stability for Nonlinear Fractional Functional Differential Equation
title_full_unstemmed On Local Generalized Ulam–Hyers Stability for Nonlinear Fractional Functional Differential Equation
title_sort on local generalized ulam–hyers stability for nonlinear fractional functional differential equation
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2020-01-01
description We discuss the existence of positive solution for a class of nonlinear fractional differential equations with delay involving Caputo derivative. Well-known Leray–Schauder theorem, Arzela–Ascoli theorem, and Banach contraction principle are used for the fixed point property and existence of a solution. We establish local generalized Ulam–Hyers stability and local generalized Ulam–Hyers–Rassias stability for the same class of nonlinear fractional neutral differential equations. The simulation of an example is also given to show the applicability of our results.
url http://dx.doi.org/10.1155/2020/3276873
work_keys_str_mv AT dongmingnie onlocalgeneralizedulamhyersstabilityfornonlinearfractionalfunctionaldifferentialequation
AT azmatullahkhanniazi onlocalgeneralizedulamhyersstabilityfornonlinearfractionalfunctionaldifferentialequation
AT bilalahmed onlocalgeneralizedulamhyersstabilityfornonlinearfractionalfunctionaldifferentialequation
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