Existence and Uniqueness of Nonlocal Boundary Conditions for Hilfer-Hadamard-Type Fractional Differential Equations (1802.04262v2)

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^{\alpha,\beta}x(t)+f(t,x(t))=0, \hbox{ on the interval } J:=(1,e]] with nonlinear boundary value problems [x(1+\epsilon)=\sum{i=1}^{n-2}\nu_{i}x(\zeta_{i}), \quad\quad\quad~{H}D^{1,1}x(e) = \sum{i=1}^{n-2} \sigma_i~{H} D^{1,1}x(\zeta{i})]