Analysis of multi-term time complex fractional diffusion equation with Hilfer-Hadamard fractional derivative

This work deals with some new results for existence, uniqueness, and Ulam-Hyers types of stability of the solution of multi-term time complex fractional diffusion equation using Hilfer-Hadamard fractional derivative. We prove the existence and uniqueness of the solution by employing Schaefer’s fixed point theorem and Banach fixed point theorem. Further, we present Ulam-Hyers type stability of the solution of multi-term time complex fractional diffusion equation. Moreover, we discuss the boundedness and interchange properties of the Hilfer-Hadamard fractional operator.