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

Abstract

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.

Keywords

• hilfer fractional derivative
• ulam stability
• pantograph differential equation
• nonlocal integral condition