In this paper, we consider a class of boundary value problems of fractional differential equations with integral and anti-periodic boundary conditions, which is a new type of mixed boundary condition. By using the contraction mapping principle, Krasnosel’skii fixed point theorem, and Leray-Schauder degree theory, we obtain some results of existence and uniqueness. Finally, several examples are ...

This article presents a study of the existence and uniqueness solutions for system hybrid fractional differential equations involving derivatives Caputo-Hadamard type with three-point boundary conditions. In addition to this, “Hyres–Ulam” stability this equation is verified, finally numerical example was presented support our theoretical results.

In this article, we establish new Lyapunov-type inequalities for third-order linear differential equations y′′′ + q(t)y = 0 under the three-point boundary conditions y(a) = y(b) = y(c) = 0 and y(a) = y′′(d) = y(b) = 0 by bounding Green’s functions G(t, s) corresponding to appropriate boundary conditions. Thus, we obtain the best constants of Lyapunov-type inequalities for three-point boundary v...