Existence and uniqueness of nonlocal boundary conditions for Hilfer–Hadamard-type fractional differential equations

Abstract

In this paper, we use some fixed point theorems in Banach space for studying the existence and uniqueness results for Hilfer–Hadamard-type fractional differential equations Dα,βHx(t)+f(t,x(t))=0 on the interval (1 , e] with nonlinear boundary conditions x(1+ϵ)=∑i=1n−2νix(ζi),HD1,1x(e)=∑i=1n−2σiHD1,1x(ζi).