Sharp estimates for the unique solution of the Hadamard-type two-point fractional boundary value problems

Abstract

In this short note, we present the sharp estimate for the existence of a unique solution for a Hadamard-type fractional differential equations with two-point boundary value conditions. The method of analysis is obtained by using the integral of the Green's function and the Banach contraction principle. Further, we will also obtain a sharper lower bound of the eigenvalues for an eigenvalue problem. Two examples are presented to clarify the applicability of the essential results.

arXiv comment7 pages, Received 24 April 2020, accepted for publication in "Applied Mathematics E-Notes"