**Idris Ahmed 1,2,3, Poom Kumam 2,4,***∗***, Kamal Shah 5,6, Piyachat Borisut 1,2, Kanokwan Sitthithakerngkiet <sup>7</sup> and Musa Ahmed Demba 1,2,8**


Received: 27 November 2019; Accepted: 18 December 2019; Published: 7 January 2020

**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

**MSC:** 26A33; 34A34; 34D20; 34A12
