On the non-local \varphi -Hilfer hybrid fractional differential equations: an existence study

In this paper, we examine the existence of solutions for a hybrid fractional differential equation involving the \varphi-Hilfer derivative with a non-local condition. First, we establish the equivalence between our problem and an integral equation. Then, we utilize Dhage's renowned fixed-point theorem to prove the existence of solutions. Finally, we present an illustrative example to validate our results.

کلیدواژه ها:

Hybrid fractional differential equation ، \varphi -Hilfer derivative ، Non-local condition ، fixed point theorem