Nonlocal and multiple-point fractional boundary value problem in the frame of a generalized Hilfer derivative

Abstract The aim of this manuscript is to handle the nonlocal boundary value problem for a specific kind nonlinear fractional differential equations involving ξ -Hilfer derivative. used operator generated by kernel $k(\vartheta,s)=\xi (\vartheta )-\xi (s)$ k ( ϑ , s ) = ξ − and differentiation ${ D}_{\xi } = ( \frac{1}{\xi ^{\prime }(\vartheta )}\frac{d}{d\vartheta ) $ D 1 ′ d . existence uniqueness solutions are established considered system. Our perspective relies on properties generalized Hilfer derivative implementation Krasnoselskii’s fixed point approach Banach’s contraction principle with respect Bielecki norm obtain solution bounded domain in Banach space. Besides, we discuss Ulam–Hyers stability criteria main Finally, some examples given illustrate viability theories.