A Class of ψ-Hilfer Fractional Pantograph Equations with Functional Boundary Data at Resonance - Bingzhi Sun; Shuqin Zhang; Tianhu Yu; Shanshan Li (Fractal and Fractional)
In this paper, we explore the outcomes related to the existence of nonlocal functional boundary value problems associated with pantograph equations utilizing <semantics>ψ</semantics>-Hilfer fractional derivatives. The nonlinear term relies on unknown functions which contain a proportional delay term and their fractional derivatives in a higher order. We discuss various existence results for the different “smoothness” requirements of the unknown function by means of Mawhin’s coincidence theory at resonance. We wrap up by providing a detailed explanation accompanied by an illustration of one of the outcomes.