On the \(\Phi\)-Hilfer iterative fractional differential equations

To avoid studying iterative differential equations with distinct fractional order derivatives it is essential to treat them with a broad fractional derivative, which leaves other fractional derivatives as a special case. In this way, we study an initial value problem for non linear iterative fractional differential equations involving \(\Phi\)-Hilfer fractional derivative. We establish the existence and uniqueness of the solution through fixed point theorems. We prove results concerning the dependence of solution and Ulam-Hyers stability of the problem. Finally, we present an example for illustration to demonstrate our outcome.