On $\psi$-Hilfer fractional differential equation with complex order

Abstract

The objectives of this paper is to investigate some adequate results for the existence of solution to a $\psi$-Hilfer fractional derivatives (HFDEs) involving complex order. Appropriate conditions for the existence of at least one solution are developed by using Schauder fixed point theorem (SFPT) to the consider problem. Moreover, we also investigate the Ulam-Hyers stability for the proposed problem.

Keywords

• fractional derivative
• existence
• ulam-hyers-rassias stability
• complex order