Stability Results for Implicit Fractional Pantograph Differential Equations via <i>ϕ</i>-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition
This paper presents a class of implicit pantograph fractional differential equation with more general Riemann-Liouville fractional integral condition. A certain class of generalized fractional derivative is used to set the problem. The existence and uniqueness of the problem is obtained using Schaef...
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doaj-fa90cb3edaa04610b26b46941ee0290b2020-11-25T01:42:27ZengMDPI AGMathematics2227-73902020-01-01819410.3390/math8010094math8010094Stability Results for Implicit Fractional Pantograph Differential Equations via <i>ϕ</i>-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral ConditionIdris Ahmed0Poom Kumam1Kamal Shah2Piyachat Borisut3Kanokwan Sitthithakerngkiet4Musa Ahmed Demba5KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandCenter of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandDepartment of Mathematics, University of Malakand, Chakadara Dir(L), Khyber Pakhtunkhwa 18800, PakistanKMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandIntelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, ThailandKMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandThis paper presents a class of implicit pantograph fractional differential equation with more general Riemann-Liouville fractional integral condition. A certain class of generalized fractional derivative is used to set the problem. The existence and uniqueness of the problem is obtained using Schaefer’s and Banach fixed point theorems. In addition, the Ulam-Hyers and generalized Ulam-Hyers stability of the problem are established. Finally, some examples are given to illustrative the results.https://www.mdpi.com/2227-7390/8/1/94hilfer fractional derivativeulam stabilitypantograph differential equationnonlocal integral condition |
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DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Idris Ahmed Poom Kumam Kamal Shah Piyachat Borisut Kanokwan Sitthithakerngkiet Musa Ahmed Demba |
spellingShingle |
Idris Ahmed Poom Kumam Kamal Shah Piyachat Borisut Kanokwan Sitthithakerngkiet Musa Ahmed Demba Stability Results for Implicit Fractional Pantograph Differential Equations via <i>ϕ</i>-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition Mathematics hilfer fractional derivative ulam stability pantograph differential equation nonlocal integral condition |
author_facet |
Idris Ahmed Poom Kumam Kamal Shah Piyachat Borisut Kanokwan Sitthithakerngkiet Musa Ahmed Demba |
author_sort |
Idris Ahmed |
title |
Stability Results for Implicit Fractional Pantograph Differential Equations via <i>ϕ</i>-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition |
title_short |
Stability Results for Implicit Fractional Pantograph Differential Equations via <i>ϕ</i>-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition |
title_full |
Stability Results for Implicit Fractional Pantograph Differential Equations via <i>ϕ</i>-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition |
title_fullStr |
Stability Results for Implicit Fractional Pantograph Differential Equations via <i>ϕ</i>-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition |
title_full_unstemmed |
Stability Results for Implicit Fractional Pantograph Differential Equations via <i>ϕ</i>-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition |
title_sort |
stability results for implicit fractional pantograph differential equations via <i>ϕ</i>-hilfer fractional derivative with a nonlocal riemann-liouville fractional integral condition |
publisher |
MDPI AG |
series |
Mathematics |
issn |
2227-7390 |
publishDate |
2020-01-01 |
description |
This paper presents a class of implicit pantograph fractional differential equation with more general Riemann-Liouville fractional integral condition. A certain class of generalized fractional derivative is used to set the problem. The existence and uniqueness of the problem is obtained using Schaefer’s and Banach fixed point theorems. In addition, the Ulam-Hyers and generalized Ulam-Hyers stability of the problem are established. Finally, some examples are given to illustrative the results. |
topic |
hilfer fractional derivative ulam stability pantograph differential equation nonlocal integral condition |
url |
https://www.mdpi.com/2227-7390/8/1/94 |
work_keys_str_mv |
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