In this paper, using two different methods, we studied an open problem and obtained several results for Lyapunov-type and Hartman-Wintner-type inequalities for a Hadamard fractional differential equation on a general interval [a,b] , (1 a < b) with the boundary value conditions.

No abstract

In this short note, we present the sharp estimate for the existence of a unique solution for a Hadamardtype 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.

This article investigates a nonlinear fractional Caputo-Langevin equation subject to the multi-point boundary conditionswhere 0 < α, β ≤ 1 and 1 < α + β < 2, c D α denotes the Caputo's fractional derivative. Some new existence and uniqueness results are obtained by applying standard fixed point theorems.