Oscillatory behavior of Ψ$$ \Psi $$‐Hilfer generalized proportional fractional initial value problems

Abstract

This paper deals with the oscillatory behavior of the ‐Hilfer generalized proportional fractional initial value problem. Using the Volterra integral equation and Young's inequality, we establish sufficient conditions for each solution of the problem to oscillate. For the appropriate choice of the kernel , our obtained results generalize and recover some existing results in the literature. Additionally, we present some examples to emphasize the importance of our results.