In this paper we study existence results for initial value problems for hybrid fractional integro-differential equations. A couple of hybrid fixed point theorems for the sum of three operators are used for proving the main results. Examples illustrating the results are also presented. MSC: 34A08; 34A12

We establish some new noninstantaneous impulsive inequalities using the conformable fractional calculus.

In the present article, we study a new class of sequential boundary value problems of fractional order differential equations and inclusions involving ψ-Hilfer fractional derivatives, supplemented with integral multi-point boundary conditions. The main results are obtained by employing tools from fixed point theory. Thus, in the single-valued case, the existence of a unique solution is proved by using the classical Banach fixed point theorem while an existence result is established via Krasnosel’skiĭ’s fixed point theorem. The Leray–Schauder nonlinear alternative for multi-valued maps is the basic tool to prove an existence result in the multi-valued case. Finally, our results are well illustrated by numerical examples.

We investigate new results about Lyapunov-type inequalities by considering hybrid fractional boundary value problems. We give necessary conditions for the existence of nontrivial solutions for a class of hybrid boundary value problems involving Riemann-Liouville fractional derivative of order 2 < α ≤ 3. The investigation is based on a construction of Green's functions and on finding its corresponding maximum value. In order to illustrate the results, we provide numerical examples.

In this paper, we study the existence and uniqueness results for noninstantaneous impulsive fractional quantum Hahn integro-difference boundary value problems with integral boundary conditions, by using Banach contraction mapping principle and Leray–Schauder nonlinear alternative. Examples are included illustrating the obtained results. To the best of our knowledge, no work has reported on the existence of solutions to the Hahn-difference equation with noninstantaneous impulses.