Stability Results for Implicit Fractional Pantograph Differential Equations via <i>ϕ</i>-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition

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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Bibliographic Details
Main Authors: Idris Ahmed, Poom Kumam, Kamal Shah, Piyachat Borisut, Kanokwan Sitthithakerngkiet, Musa Ahmed Demba
Format: Article
Language:English
Published: MDPI AG 2020-01-01
Series:Mathematics
Subjects:
hilfer fractional derivative
ulam stability
pantograph differential equation
nonlocal integral condition
Online Access:https://www.mdpi.com/2227-7390/8/1/94
Description
Summary: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&#8217;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.
ISSN:2227-7390

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