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

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 (H)D(alpha,beta)x(t)+f(t,x(t))=0 on the interval (1,e] with nonlinear boundary conditions x(1+epsilon)= Sigma(n-2)(i=1)nu(i)x(zeta(i)), (H)D(1,1)x(e)= Sigma(n-2)(i=1)sigma(iH)D(1,1)x(zeta(i)).

Automated summary

This paper utilizes fixed point theorems in Banach space to study the existence and uniqueness results of Hilfer-Hadamard-type fractional differential equations on the interval (1,e], with nonlinear boundary conditions included.