Existence and Uniqueness of Nonlocal Boundary Conditions for Hilfer-Hadamard-Type Fractional Differential Equations

Abstract

In this paper, we used some theorems of fixed point for studying the results of existence and uniqueness for Hilfer-Hadamard-Type fractional differential equations, \[_{H}D^{α,β}x(t)+f(t,x(t))=0, \hbox{ on the interval } J:=(1,e]\] with nonlinear boundary value problems \[x(1+ε)=\sum_{i=1}^{n-2}ν_{i}x(ζ_{i}), \quad\quad\quad~_{H}D^{1,1}x(e) = \sum_{i=1}^{n-2} σ_i~_{H} D^{1,1}x(ζ_{i})\]

17 pages. arXiv admin note: text overlap with arXiv:1801.10400