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...
Main Authors: | , , |
---|---|
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 |
id |
doaj-0f68aa1a4f9148258a75d5c76363779d |
---|---|
record_format |
Article |
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 |
_version_ |
1715082323246972928 |