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.
Zerbib, S. , Hilal, K. and Kajouni, A. (2025). On the non-local $ \varphi $-Hilfer hybrid fractional differential equations: an existence study. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2025.63952.2874
MLA
Zerbib, S. , , Hilal, K. , and Kajouni, A. . "On the non-local $ \varphi $-Hilfer hybrid fractional differential equations: an existence study", Computational Methods for Differential Equations, , , 2025, -. doi: 10.22034/cmde.2025.63952.2874
HARVARD
Zerbib, S., Hilal, K., Kajouni, A. (2025). 'On the non-local $ \varphi $-Hilfer hybrid fractional differential equations: an existence study', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2025.63952.2874
CHICAGO
S. Zerbib , K. Hilal and A. Kajouni, "On the non-local $ \varphi $-Hilfer hybrid fractional differential equations: an existence study," Computational Methods for Differential Equations, (2025): -, doi: 10.22034/cmde.2025.63952.2874
VANCOUVER
Zerbib, S., Hilal, K., Kajouni, A. On the non-local $ \varphi $-Hilfer hybrid fractional differential equations: an existence study. Computational Methods for Differential Equations, 2025; (): -. doi: 10.22034/cmde.2025.63952.2874
)